I have the pleasure to introduce Rüdiger Weiss, he's a computer science professor from Berlin and his PhD student, Bruno.  Maybe it's kind of a hobby for a mathematician to motivate people to have a different view on math. And what I want to present with my colleague, Bruno Kirschner, today is some combination of very hard mathematics, very nice but very genuine mathematics and how to combine it in existing application to provide a better way to protect social interaction and even provide something like authenticated anonymity. Let's start with one of my favorite quotes from Bruce Schneier. Draster mass encryption is your friend. If you make then a logical evaluation of the situation, you can say in some kind of thinking mass might be your friend when you want to project your privacy against biotrapping and secret agents, these which biotrapping all, maybe all, or almost all the traffic around us. There is cryptography, the one protection which helps. I think it's a very nice or at least interesting fact that if you take a look on the situation that the government are not able or not willing to protect their people from secret agencies from other countries to biotrap, all the information they present on the internet. And if you use encryption, you can make really a game changer because if you use appropriate cryptography, this is a very strong protection for your privacy. And we want to extend this in some direction to protect social interaction and enable totally new trust models. Let's start with the stuff we have integrated our protocols and the old protocols in. That is elliptical curves. And allow me to give an introduction. And the introduction is very funny. It's a statement from Gauss, I stated by Hardy now, which said that if mathematics is a queen of science, the theory of numbers is the queen of mathematics. And it's also very interesting because of what? Because of its supreme uselessness. So very clever mathematicians have made a statement that number theory is something which is very poor and very useless. And now we are in a situation that number theory is one of the really main technology if we want to protect our privacy in the internet. And let's make this claim in another direction and make a short statement to say that elliptical curves are because of their supreme non-uselessness can be seen as queens of practical theory of numbers. So I want to make the statement that if you think mathematical problems are very challenging, take into consideration that the theory of numbers is around the mathematician as one of the hardest fields of this science. And in this very hard science, elliptical curves are really some of the very challenging candidates for research. And so we really connect us to a very special kind of mathematics if you use elliptical curves. And if you have listened to my talks in former camps on the CCC convention, you know that I'm a bit critical in some aspects of elliptic curve. Nevertheless, elliptical curves have a lot of interesting properties. And one of the very important in the practice is that it's using strata key lengths. And so we have the situation that in a lot of embedded systems, in a lot of personal devices, and also in the field of cryptocoins, there is a very heavy use of elliptical curve cryptography. And this is the case, even though there are at least three problems. One I mentioned first is it's very hard mass. That is so hard mass that only a few men and women can really evaluate elliptical curve in an appropriate way. Second point is that it's interesting if you think about embedded systems, you need very strong random on every signature you have to perform. This is something which is usually a big problem if you have embedded systems where it's very hard to get random bits. And the last point is beware of quantum computing. And I have to acknowledge that when I make the statement that elliptical curves have really very big problems if you have quantum computing, usually that was some statement. I was not so sure if it's fair in a specific way because we don't know the actual state of the research in the field of quantum computing. But in 2017, there was a really very nice statement from Coplitz and Menace, a riddle rubbed in Enigma. And this is very interesting because they were discussed in a lot of pages why it might be not a good idea to switch to elliptic curves regarding the problems with quantum computing. And I make only one quote. And this quote says that the NSA has really a statement that they prefer, as are 3072, because it's more resistant against quantum computer attacks than the usually used ECC 256 and maybe also ECC 384. And really the main statement is when we have quantum computers, then the attacking possibility is very closely related to the length of the keys. And so I would make the statement that even elliptical curves with 512 bits will not provide the same security than as are 4096. 3072 maybe also, but there would have to make some deeper evaluation. So I make the statement that it's now pretty content that elliptical curves might have big problems if we have a breakthrough in the field of quantum computing. So it's very interesting also to evaluate cryptocurrency which use elliptical curves. And I have a good news. There is a lot of features in Bitcoin which make attack with quantum computers not so problematic than in a lot of other fields. Nevertheless, elliptical curves are interesting, are wisely used, but nevertheless take also the problems into the consideration. But I have also a good news. I told you that we have elliptical curve which is very hard mass. And I have advised the diploma thesis in mass regarding elliptical curve in 1999. That's 20 years ago. And I have still not the feeling that I have a sufficient understanding of elliptical curve that I could present, for instance, a new elliptical curve for cryptographic proposals. And so I want really to state that it's very complicated mass. So coming to the second point, we use blind signature. And there I have a good news, but because blind signatures are really very easy to understand. Even in a normal exercise in cryptography, you can present it within the first two months. And this simplicity really has a lot of nice properties. For instance, the security proofs are very understandable. And blind signatures are mainly introduced by David Schaum in crypto 1982 and had a first implementation in DigiCash, a company which has been founded by Schaum and was the first really anonymous digital cash system. Interesting from a cryptographic standpoint is that we really integrate a very new trust model. And we can this trust model use in the field of electronic voting and very actual, if you see some secure mixing providers, use it for providing anonymity for cryptographic coins. And this was our idea. We have elliptical curves in a lot of fields. We may be a bit critical and not too enthusiastic about elliptical curves. Nevertheless, it's in heavy use. And as a resorter and as a hacker, it's interesting to play around with existing technology. And though we had really the idea to make really blind signature using also in the field of elliptical curves, and especially in open P2P. And this was a very fantastic work by my student and now colleague Bruno Kirschner. And we will present it in the second part of this talk. Yeah, thank you very much for having me. OK, Mr. Tom. OK, yeah, thank you for the introduction. As really just told you, my part in this was that using blind signatures somehow or giving blind signatures more to the open world was part of my master thesis a few years ago. So I'm first giving you a short introduction how blind signatures actually work, or even better, what is the idea behind blind signatures? Because normally if you try to speak with someone about it, they haven't heard about it or don't have a clue what's actually going on. So the first idea you normally give to someone is the real-world example, how you would do it without electronics. And there you would take something you would want to have signed, but the person will have to sign it, actually should not know what is on this letter. So you take the letter, put it in an envelope, and you also take a piece of carbon paper to it so that as soon as the person gets the closed envelope, he or she can sign the outside of the envelope and the carbon paper will actually copy the signature onto the letter inside. Then you can hand back the envelope you open it and you have a sheet of paper with a signature. The idea for blind signatures is actually to do the same in electronics. So we need something that allows us to encrypt data so that it's not that you can't read it. Then put a signature on it, decrypt it, and have some kind of data with a valid signature on it. And this is what you can see in the graphics. This has some problems, because normally you don't want to sign something you don't know. If you sign something you don't know, it can happen really quickly that you sign something bad or that you lose something you actually want to still own. So you want to verify that the person who you're going to interact with is only handing you in valid information or something context relevant. So you could just say, we are doing an election inside our company and you're only allowed to vote.  But as soon as you get into a bigger context, this doesn't work. And also another fact is that normally you don't want this signer to know who you actually are. Because it could happen that just from the case that he knows who's going to take part in an election or in something else, going to sell something if you go into the idea of cryptocurrencies, he can take advantage of this fact. So you introduce a third party, the Identity Broker, which you use to authenticate against. So you authenticate against the Identity Broker. He or she will hand you in a certificate and the signer will only know the public key to verify this kind of certificate. So as soon as you take part in the election or whatever else you want to do, you can just take a hand in the envelope and show the certificate. And the signer can go and verify the certificate and say, that's fine. I will go and work with it. Another way, if you don't want to introduce the Identity Broker, is that you can actually only do if you want to sign data that is somehow randomized. Then you could say, just hand me in 100 envelopes. I will open 99 of them. Look inside. And if 99 of them somehow match the kind of data I would expect, I will sign the 100. But this only works if the piece of data inside is somehow randomized. Like, I want to have a pseudonym. And I doesn't care about if there is a prefix or suffix or whatever. It's just completely garbage. And I want to have one of them to take part in an election, for example. The next thing, OK, we have this idea of blind signatures. How can we spread them? Or other people said the idea of blind signatures. And how can we actually spread them? And so we thought about how do you spread a good idea? First thing is you could make it simple to understand. So try to explain it and just push the idea into the heads of other people. The other thing is you could simplify it as much as possible that other people are going to implement it somewhere else. And the third thing is show that it's easy to inject and already existing standards. Or at least show that it's very easy to change the existing standards in a minimal invasive way that you can use it in. And there we moved over to OpenPGP. Because we thought, especially for email encryption and decentralized communication, it's a very common used way. It's still not an official standard, but it's a de-facto standard. Because if you want to use, if you want to encrypt emails or other decentralized communication in the last 20 years, it was the way to go. And there we decided, OK, if you want to show that it's easy to integrate and it's easy to use, it should be flexible. So we, especially someone who wants to have signed data, shouldn't be forced to create a new key pair or do something else, just reuse whatever already exists. And we should try to avoid to change the signature definition of OpenPGP so that you can go and everything you have looks like a typical key signature or data signature or whatever. And there should be almost no difference. And yeah, then we looked into OpenPGP and we decided that there's actually one thing you need to add to make it somehow possible. And this is the blinding scheme you actually want to use. Because blinding schemes are almost identical to the typical signature schemes, like the signature scheme you use for RSA or ECDSA. But sometimes you run into blinding schemes which need to somehow change definition of how to verify the signature in the end. And if you want to also maybe add them later or allow to use them, the signature must somehow state that which blinding scheme you actually used. But if you want to allow the key reuse, you don't want to introduce a new public key scheme and new signature scheme for every blinding scheme, because sometimes you can reuse a key for ECDSA, for example, for different blinding schemes. And therefore it wasn't necessary to introduce a small change. Here you can see how a typical signature in OpenPGP is actually built up. It's quite easy. The top part is some metadata, like the version you used, the signature type, the PAKDP algorithm, and other stuff. This is just meta information of the signature. And then you have three other parts. The stuff in the bottom is the signature itself, so the design data. The most interesting part, at least for this work, was the different kinds of sub-packets. We have unhashed sub-packets and hashed sub-packets. The unhashed stuff is also just additional, yeah, it's not metadata, it's additional data you can add, but it's just not necessary to verify the signature. So you don't need this information to check if the signature is valid or not. More interesting are the hashed sub-packets. These are all information you somehow want to have if you want to verify a signature, like when was the signature created, was it already valid at a specific point in time, or which blinding scheme actually was used, and other stuff. So we decided that the blinding scheme should be part of the hashed sub-packet, because there we can ensure that if someone wants to manipulate it, the signature wouldn't verify anymore, because it was changed. Yeah, this is, yeah, command line interface output. It's mostly not interesting in here. You can just see that all the stuff you already had on the slide before is outputted on the command line. You have the sub-packets in the middle. There is, for example, the hashed sub-packet with an ID of two. This is the signature creation date. And then the red highlighted one is the new introduced one. It's a critical hashed sub-packet in this time. Critical means in here that if your implementation of OpenPGP doesn't know it, it will recognize that it can't verify this kind of signature, and it will notice you that it wasn't able to verify the signature because it didn't understand the specific change. If it not marked as critical, it could try to avoid, it could just try to ignore the information, and this is not what we want in here. Next to then, it's number 100 because it's marked as experimental. And we decided to use an ID, so the ID here you can see is number one, which is an ECDSA-based blinding scheme. There was also number zero, which is for all blinding schemes which use the same verification method they would use if you don't have blinding, just a typical signature. Yeah, and most important here is that for a user who actually received a blind signature which was created through a blinding scheme, there is no difference in verifying that the signature is valid or not. He or she will just use the normal command line interface or programming interface, whatever actually is. It's the signature in there and it's the signature valid. So the line at the bottom, the signature one, was one created through blinding. Yeah, the information is still online. It's a few years old. I tried to get it back working in the last days. It's still not totally done because for some reasons I decided to do it with web technology. Web technology is moving fast. It's not working after four years. So yeah, feel free to look into. Thanks a lot and I want to really close with a statement of Edward Snowden some years ago. Maybe I have presented on the last camp. CryptoWorks, it's not a black art. It's a basic protection and we must implement it and active research in it. And this is, I think this is a very challenging task for researchers and hackers. As I mentioned, if you want to protect your citizen in a state against really unlawful interaction from the outside, then in a political system, I make really the jokes four years ago. The government is not willing or not able to protect European citizen against US and other secret agencies. And I have to acknowledge that after the change in the government in the United States, the situation has not become better. So the discussion we will maybe have in the field of Bitcoin, if we should trust mass or more than our government, I think in the field of protecting our privacy, we don't have to make evaluation. It's very clear that we have the situation that unlawful secret agencies wiretrap citizen in other states. It's not unlawful for them. They have special law that citizen of countries which are not the place of the headquarter of the secret agencies are much less protected. This is also in Germany the case. But if you make really the statement that every government can spy on every other government, you say, even if our government not misbehave, we have problems with so many other agencies. And it's very clear. And we have really also results in politics that sometimes agencies are their friends in other agencies. If they want to do actions against citizen, they are not allowed. They tried to make it possible if they cooperate with other secret agencies. And to make a very clear statement, crypto is a protection. You have only trust in mass. And this is open science. And the best results in cryptography come from public research. And so this is really a very important business protection. And what I stated out here, we have a lot of advanced crypto protocol where we can really modify new trust models. If you take a look at the old protocol of digit gas and electronic voting, you'll find a lot of surprising ideas really doing really strange or almost magical stuff. So if you just make the idea, we can provide a really private electronic coin. An electronic coin you can duplicate as much as you want. And making this possible in a field of DigiCash with blind signature is really amazing. And what's even more amazing, I make a lot of statements in the first part of the talk that elliptical curves are very hard to understand cryptographic constructs. Blind signature are not very hard to understand and are not very hard to implement and really provide another level of protection for many social interactions. And though I really want to invite you to take a look on the mass, as I told you, elliptical curve is maybe with a hard starting point. But blind signature is really pretty easy to understand. And easy to understand is not only good to implement. It's also good for mathematicians because they can really prove very easily properties of this field. And to make it very short, blind signatures are understood, are easy to implement, and have provable security margins. You have to take a close look what you have exactly proven. And you just talk about proof and secure cryptography. Nevertheless, blind signature build a very interesting level. And I had some years ago where we have the funny and this time very successful private party. They have really discussed about participation with liquid feedback and so on. And really, there is a lot of cryptographic research which is in the market since the 80s or the 90s, which we can really use to improve privacy and making a lot of stuff possible. And so really, the two methods we have, cryptography is very important, integrated wherever it's possible. And this is one thing I'm a bit more optimistic on in a lot of other fields. If I compare it with our last talk on the camp four years ago, I have to acknowledge that cryptography has been grown in a lot of fields. Using HTTPS is not a very exotic hacker hobby anymore. And also a lot of instant messaging using very good, publicly evaluated cryptography. Something I just, it's so simple and so understandable for a lot of people. Not only in the hacker community is that we should use everything as open source. And of course, also Bruno's work is open source. So take it, improve it, and think about really problems. One of my favorite PhD thesis I've read was a thesis from a student which provided, I think, 1.6 million different signature schemes. So blind, blind verification and so on. And make a statement, now we have 1.6 million different schemes. We are heavily looking for application to use it. And this is also my statement. If you rethink trust models and really a trust model where you can, you must, the certifications agency, you have not to trust them that they record your key number they have signed because they don't have it. And if you make really a certification with this protocol, it's also a legal protection for the certification agency in some scenarios. And really you can use a lot of practical problems just using the right living time of keys, using different keys for different property. And what I really want to make a statement is that we should continue in this work. And if you work in other fields, if you think about new trust models and new social interaction, talk to your local cryptographer because they have a really rich box of tools lying around. And a good starting point is, as I mentioned, blind signatures because they are pretty easy to understand and are very powerful to use. Thank you for your attention. Thank you, Julian Bruno. And we have a lot of time for Q&As. So there are microphone angels. One is over there. And there's none other. So signal to him or just walk over to him. That wasn't a wave. That was a dog wagging its tail. There's one. So what technologies other than blind signatures do you see as being important in this field, which recently have lost patent protection and were discovered a long time ago? Zero knowledge, for instance. This is a whole family, which I also would enjoy to present here. But it's a bit more difficult, Maas. The idea is you can prove some properties without presenting your secret. And this is, for instance, losing Zcash, for instance. There are some applications in the outside. And real history knowledge protocols are very interesting points. But for mathematical standpoint, much more involving than the protocol represented here. Here is just some simplification. It's just a multiplication with a random number. And exponentiation. The main proofs are very easy to understand and a good starting point. If you are then you have enjoyed this challenges, take a look on zero knowledge. There is really about 20, 30 protocols which are interesting and should be implemented. And it's a bit scary that they make a small field in this thing with the technologies from 1982. And I think that was at least one of the first implementation in 2016 or 2015? 16. 16. As you see, more than 30 years. And really, this is my request for the mathematician. Try to communicate it more and maybe only a bit simplified and start with a thing. But on the other side, people which have the questions, how we can improve, for instance, electronic cash protocols. I give a talk about different blockchain construction the day after tomorrow. And it's very clear you have the situation that in a public blockchain, every transaction is readable until the end of time. And if you don't use cryptographic solution, it's a complete nightmare. And even if people say, yeah, OK, Secret Agency might not intact me if there are data and if the agency is in, then I have to acknowledge that some hackers have not the high moral standpoints we have. There are really, in short, if a Secret Agency can hack it, other people can hack it too. And this is a really dramatic game changer. And if you do something like Mpenza or Libra or even Bitcoin, you can wake up in a completely privacy nightmare. And so I think you have, even in the field of cryptocurrency, a responsibility to provide privacy on the lowest level. And here is really a very good low level. We are here at the bits. We make manipulation on the bit layer. And you can not attack in this layer. We protect one layer. There are a lot of other problems. But this layer is mathematically protected. And this is a good way to do things like that. OK. Yeah, you explained the idea of the blind signatures. I'd like to know a little bit more how it's actually doable. Like, as I understand, probably you have something encrypted, probably with a symmetric encryption. And you want to do the signature with a symmetric encryption? No? Asymmetric encryption. Can you hear me? No, actually, there is no symmetric encryption. It's all done in the asymmetric way. So you use public-private key pairs on both sides. But mainly, you make one multiplication with a random number? Yeah, or you can also include it. But there is no symmetric encryption inside. It's no symmetric cryptography. It's the main proposal for blind signatures have been as a scheme. And in this case, it's just a multiplication with a random number. And then it's a very basic mathematical change of the formulas. And in the field of elliptical, it's a bit harder, but not much. OK, any more questions from the crowd? And maybe from the internet? Big? There's one question from the audience. Have you seen any interesting applications of blind signatures in recent years? Not many. But as I stated, there are cash protocols which have not been so successful. There have been voting protocols. I think some discussion and one clear statement. I'm even with strong cryptography, I'm not a friend of electronic voting. I think there's a good place to stay on paper. And if somebody which laughs mass, which laughs cryptography statement, it's better to make election with a paper way, something we know since decades and centuries. It's a good idea. In crypto, we can solve a lot of problems, but these problems are not the main problems where we are against electronic voting systems. Nevertheless, cryptographic solution can make electronic voting screens much more secure than the actual situation outside. But nevertheless, I see the practical problems there as so important that we should not mess around with voting. Voting is from a philosophical standpoint, the only point, the only spiritual point where we distribute power in a democracy. And we should not mess around with this. Last statement, as I mentioned, maybe if you take a look in actual mixing schemes for digital currency, there are some protocols which use in blind signatures. So not many, but some application using blind signatures outside. And we hope we can improve that because this is a reason why we have chosen OpenPGP as a worldwide accepted standard.  OK, any more questions from the audience? That's not the case. Then thank our speakers again with a one round of applause.


In the previous video, we saw a counter example of a subset of a group that could not be a subgroup, not every subset will be a subgroup of a given group. There are some conditions that have to be met, right? The subset itself has to be a group using the operation that's already on the group, but with restriction. This idea of restricting the operation to a subset, if this is done successfully, this is referred to as the closure property. That will say things like, oh, the subset H is closed under multiplication. If whenever you take a product of two things in H, it lands back in H itself. So if G and H are in H, then G times H is in H as well. This is called the closure property. If H is a subgroup, then restriction of the binary operation to H, if that is also an operation in H, that means that H is closed under the operation. That's an important principle here. And so with that in mind, a subset is a subgroup. You know, by definition, that means it's a group inside of a larger group using the same operation. But that can be kind of difficult to show at times. Alternatively, we're going to see in this proposition, there are three alternative conditions we can check to see when a subset is a subgroup or not. So the first one, like I already mentioned, is this closure principle, that the product of any two elements in the subset lands in the subset itself. G or H is closed under the multiplication. To be a subgroup, you also have to contain the identity. So the identity has to be inside of H. And given any element in H, the inverse of that element must also be H. So these things, we say things like this first principle to emphasize, you might say that it's closed under your operation, which we'll just call it multiplication to be general. It's closed under multiplication. You might say that for property B that the set is closed under the identity, which, you know, that just means I did the identities in there says no one usually says it that way, but you could if you wanted to. The last principle, we often say that it's closed under inverses, because you can think of like the inverse map as this unary operation that is just a function with one input. And so our set H has to be closed under that function as well that have taken the element when you restrict the inversion map to the to the set that will also give you that it will restrict properly so that inverses are always contained in there. So I, I claim this is an if and only of statement right that H is a subgroup if and only if it's closed it has the identity and it has inverses. And so as it's an if and only if statement this is a this is a proof for the cost of two right we have to prove both directions. So what we're going to do first is assume that H is a subgroup. And because H is a subgroup that means it is itself a group inside of G but using the same operation as G itself. And so like I was mentioning before we started the proof that would imply that H is closed right because we have this operation G times G, which goes to G this is the group operation. If H is a subgroup then the restriction of the operation will be to H as well so we get the operation h cross H to H. And therefore, if we take elements G and H, which are in H, we see that G times H, this will have, well I should say the pair G times H would have to map to an element GH, which belongs to H. So you get the you get the closure principle pretty quickly from the definition of a subgroup. So that's pretty nice. What about the identity right. Well, H has to contain an identity if it's a group, I mean if it's a subgroup it's a group in its own right, in which case it has an identity, which means that E prime, let's call that identity E prime. So that means E prime H is equal to H E prime which is equal to H for all elements inside of H right there. This E prime potentially could be a different element from the group it's from the identity of the group right. In particular, since E prime is inside of H, it must be true that E prime times E prime is equal to E prime. This is what we refer to as an item potent element that it's square is equal to itself. This is something we see with sets all the time like the intersection of two sets. I should say the same set right the intersection is itself on the union of a set with itself is a again in a group an identity element is item potent. But in fact in a group the only item potent element is the identity itself and this is sort of going to be the problem right here that if you take an item potent element like this E prime it has an inverse right it has an inverse in the group because G is a group so it has an inverse. So what happens when we take. I, or E prime times its inverse one way times E prime times inverse well it'll give you the identity element in G right, but since E prime is item potent I can replace E prime with E prime times E prime, then by associativity you're going to multiply E prime by its inverse that'll give you the identity of G, and then E prime times E will just be E again because you're times it by the identity in G, not sure why there's two, two periods right there. But the thing is what we see here is that E is an equal to E prime. So what we've basically shown here is, this is often what's referred to in the literature as a porism. Basically, a theorem we proved while we were proving something else. So this is something to kind of note here that any, any item potent, any item potent element you know, I'm going to try to write this with my poor handwriting which is not going to do any, any favors right here. We're going to do the follow I'm going to type it. So this is our porism. It's something we proved in the proof of something else. Let G be a group. And let we'll say G be a member of G right here. And so what we've shown is the following, then an element then G is in fact item potent. If and only if G is the identity, a group only has one item potent element, and that is the identity itself the identity is clearly going to be item potent, but we've now shown that if you have an item potent element it is the identity. And so that's helpful here, because if the subgroup, if the subgroup has an identity element it will be item potent, but it's an item potent and the larger group G as well, which then means it has to be the group identity. This tells you that H has the same identity as the ambient group, which is proving this condition to be a subgroup it means to have an identity but this statement right here B is saying that it has that it contains the identity of the overgroup. So the last thing we have to do is consider inverses. But since we now know that the identity of H is the same identity as G, the inverses are going to have to be the same inverses as in G as well. So since H is a subgroup, it's a group in its own right it has inverses. So for each element H let's say that H prime is the inverse of little H in capital H. And so that means that H, H prime will equal H H prime or H prime H which is E and now this is the identity in G right. So H prime is an inverse of H, but like we've learned before inverses are unique. So if you walk like an inverse and quack like an inverse then you must be the inverse. The only element which can multiply by H inside of G to give you the identity has to be H inverse, which would imply that H prime is equal to H inverse. And this tells us that the subgroup is closed under inverses. That is the inverses in H were the same inverses in the ambient group of G. So H will have the same identity as G and it'll have the same inverses as G. Although some of those inverses will be missing because some of the elements of G are likely missing as well. So that proves the first direction. If G is a subgroup, because it's a group inside of a group, it'll be closed. It has the same identity as G and has the same inverses as G. So every subgroup will have those three properties. Now let's go the other way around. Let's suppose that H satisfies those three conditions. It's closed under multiplication. It's closed under the identity and it's closed under inverses. It contains the same identities and inverses as above. Well, since the operation is closed, this gives us a well-defined operation on H. So the closure principle is saying that we can restrict the operation to give you some type of H cross H to H. That the product of any two elements of H is well-defined, yes, but also it'll be inside of H itself. That's the important part there. So we have a well-defined operation. So we can then talk about whether that operation is going to give us a group operation or not. So the next thing to mention here is that, well, by assumption, it has an identity element. The identity of G is an identity for that operation. So we restrict it. Identity will still be an identity. And so this operation will have an identity. And because it's closed under inverses, every element in the subgroup, the potential subgroup, right, will have an inverse. So the inverse axis is satisfied as well. So basically what we have left is to worry about associativity. Why does associativity work? Well, if we take elements G, H, and K, they're inside of H. Since H is a subset of G, this means that G, H, and K are in G. So when you look at statements like G times HK, while this is a product in H, it's also, you know, it's a product in H, it's also a product in G. And in G, this operation is associative, so we can redo parentheses, like so. And so it's associative in G, which also means it'll be associative in H. There's really not much more to it. And in this situation, we often say, we say that associativity is inherited from G, because every element in H belongs to G itself. If things are associative in G, and the operation when it's restricted down to H, it'll still be associative. You don't lose properties when you restrict. And so I should mention that in this proof, it's not just associativity that would be inherited. Associativity is inherited because if the property holds for all elements in G, then certainly it still remains true for the restriction to G. This is also true for commutivity, that is, if every group, every subgroup in an abelian group is abelian necessarily, because just like associativity, commutivity of the subset is inherited from the ambience commutative group. On the other hand, though, not every subgroup in an abelian non abelian group has to be non abelian. And you might ask, why is that? Because non abelian just means that commutivity is not guaranteed. It doesn't mean that commutivity never happens. In every group, there will be some elements that commute with other elements, like the identity commutes with everything, an element will commute with its inverse, it'll commute with its powers. So there is always some commuting. A non abelian group just means that commutation is not universal, not every product will necessarily commute. But what if we restrict to a certain subset? Maybe on a subset, commutivity does in fact happen. So while properties like associativity and commutivity are inherited by any closed subset, issues about containment, like containing identities or inverse elements are not guaranteed. That's what this proof is basically trying to show us. When you check for a subgroup, you do not have to check whether the operation is associative. Because if you're closed, and the restriction of the operation is well defined, it'll be automatically associative. And if it was abelian, then the restriction will still be commutative. But the containment, like what if I take a subset? That subset, if chosen poorly, might not have the identity. It might not have inverses. So considering that a subset is likely a collection of G with some missing elements, we should be highly curious whether the elements omitted from the group G was the identity, was it inverses, or maybe there was, maybe we omitted specific products, like we took H1 and H2 but we forgot to include the product H1, H2 in the subset. So when it comes to checking whether you have a subgroup, we really just have to look for did we forget to include things like products, identities, and inverses, because properties of the operation like associativity will be inherited because our subset is closed under set operation.


పికరానియాన ఆకొిఆంి, మిలుంటింి తవంపి పి. మిష్యిఆంపి. ఆకరిన ధికరిస౩రి కాస్స్లికొికిని. అరిాస్సత్సంచాలికి. వతికరి లాయిసంపి he was suffering from a rare genetic condition, known as familial adenomatous polyposis, which predisposes not just the individual, but his entire family to developing cancers. In his case, he was initially diagnosed with the cancer of the colon, the large intestine, and during the treatment of this condition, he was also identified with cancer of the thyroid. Only once when he was cured of both these cancers did we proceed with the surgery to restore the intestinal continuity for him. He is now recovered from all the surgeries well and is returning to his home country. I wish him all the best, but I have also cautioned him to get his family members tested for this condition, in which case they would need a preventive or a prophylactic surgery. Thank you.


Alright, look at 1 Samuel chapter 13 and look at verse number 1. This is the first mention of Jonathan in the Bible and we're going to get some really important lessons for us in our lives and our relationships from the man Jonathan. But let's first look at where Jonathan is first mentioned in your King James Bible. I'm going to take a few minutes to give you one example of why we're King James only here. I don't point out, there's no way I could do a sermon on all the different mistakes in all the modern Bible versions. It would be a sermon series that went on for several weeks. So I try to point out things from modern Bible versions as we preach through them. But look at 1 Samuel chapter 13 and verse number 1 in your King James Bible. The Bible says, Saul reigned one year and when he had reigned two years over Israel. So the Bible here in verse number 1 is just saying, Saul reigned a year without incidents or without anything to note. And then it says, when he had reigned two years, so two years after he took over the kingdom, verse number 2 takes place. Saul chose him 3,000 men of Israel, whereof 2,000 were with Saul in McMash and in Mount Bethel, and 1,000 were with Jonathan in Gibeah of Benjamin. And the rest of the people, he sent every man to his tent. So right here we see the mention, the first mention of Jonathan in the Bible in verse number 2. But it's interesting to note, you know, this is the story of where Jonathan goes and he goes up against the Philistines by himself with his armor bearer. We're not going to get into that detail of that story now, but it's interesting to point out that Jonathan was leading men in verse number 2. Jonathan was a warrior, he was courageous, he was brave, and he was leading men in his father's army in verse number 2. Now I'm going to read for you 1 Samuel chapter 1 or 13 verse number 1 in the new, in the NIV, all right? Just to point out that in 1 Samuel chapter 13 verse number 1 and verse number 2, it is very easy to understand what is happening. Now let's read the NIV, all right? In verse number 1 of 1 Samuel chapter 13 in the NIV, and I hope you don't have an NIV with you tonight or this morning, but I'll just read it for you. So Saul was 30 years old when he became king and he reigned over Israel 42 years. So first of all, the NIV says Saul, I mean, I mean, it's not even close to what the King James says, all right? So it says, Saul was 30 years old and somehow he had a son that was leading warriors. When he was, so I guess he had kids when he was like 10 or something, right? I mean, if you just do the math on this, it just contradicts itself all over the place. Acts chapter 13 and verse number 21, you can turn there if you want, but it basically, that's where it tells us that Saul reigned 40 years. And here's the funny thing. If you look up Acts chapter 13 and verse number 21 in the NIV, it still says 40 years. So the NIV literally, they weren't smart enough to even, you know, make the NIV match itself, all right? So there's contradictions all over these modern Bible versions. In the NEB, it says Saul was 50 years old in verse number one. In the NASB, the New American Standard Bible, it says he was 40 years old, right? Here's the thing, the King James Bible does not say how old Saul was when he began to take over Israel. It just doesn't say, okay? But all these other Bibles, they give Saul an age when he took over the kingdom, which makes all these contradictions all over the place, all right? In the English, in the ESV, everybody loves the ESV. In the ESV, here's what it says. So first of all, what I've showed you so far is they're picking the age of Saul, and many times it's 30 years old that makes no sense as far as the age of Saul. And I'll tell you how this applies to Jonathan in just a couple minutes. But in the English Standard version, it gets even better. You're like, this is pretty good. No, it gets better, all right? In verse number one of 1 Samuel chapter 13 in the ESV, which is considered by Protestants to be, we're not Protestants, by the way. It is considered by Protestants today to be like the Bible of choice, the ESV, all right? It says, here's what it says in the ESV. Saul lived for one year and then became king. The kids are all like, yes! I can be in charge when I'm one year old. And when he had reigned for two years over Israel, then it goes into verse two. In the Dewey Reims 1899 American edition it says this, Saul was a child of one year when he began to reign. And he reigned two years over Israel. So it's wrong on both cases. But it literally says like a baby was anointed king when he was one years old.  They can't be trusted at all, all right? Remember 2 Samuel chapter five in verse number four. So now we know you're going to keep your place in 1 Samuel chapter 18. You can lose your place in 1 Samuel chapter 13. But we know that Saul reigned one year and after two years he created this army and he went to war against the Philistines. Let's get back to reality here. Look at 2 Samuel chapter five. Let's get back into this sermon about Jonathan and his relationship with King David. Look at 2 Samuel chapter five in verse number four. I just want to point out something interesting to you before we even start talking about Jonathan and David. The Bible says this. It says David was 30 years old when he began to reign. So the King James Bible doesn't tell us how old Saul was when he began to reign, but it tells us how old David was when he began to reign. So the King James Bible also tells us that Saul reigned 40 years. So what do we know about the beginning of Saul's reign? David was not born yet at the beginning of Saul's reign. So David was 30 years old when he began to reign and he reigned 40 years. So this is always pretty easy to remember that the first two kings reigned 40 years in Israel. So David was not born when Saul became king. We know this. And Jonathan was commanding men at pretty close to the beginning of his father's reign. So what does this tell us? This tells us, this kind of gives you some context to the sermon as we're going to look at it this morning. Jonathan was many years older than David. Jonathan was at least 20 years older than David, alright? Now let's look at the friendship between these two men. Why is that relevant? I don't know because I just like to see, you know, I kind of picture the relationship between David and Jonathan as kind of a mentor-mentee type relationship since Jonathan was this older warrior and David was this up-and-coming warrior and leader in the kingdom. Look at 1 Samuel chapter 18 and verse number one. Let's look at the beginning of this friendship between Jonathan and David. So 1 Samuel chapter 18, where are we at? This is right after David killed Goliath. 1 Samuel chapter 17 is when David, this young man, you know, 17, 18 years old, whatever he was, he went and he stood up and said, I will fight the Philistine.  This is one of the reasons we don't have Sunday school here because we're not going to play down these stories in the Bible. We're not going to take these stories in the Bible and turn them into a bunch of cartoons. No, David was actually a mighty man of war when he was 16, 17 years old. He was no weakling.  You know, there's no, David was a mighty man of war. He went and he killed Goliath who was nine feet tall.  That's what happened. Now right after this is when Jonathan becomes friends with David. And can't you understand why they would become friends? Jonathan was already this mighty warrior himself. He had a lot of respect for this kid. Right away he's like this, he has respect for him and he's somebody he wants to take under his wing. Look at verse number one of 1 Samuel chapter 18. The friendship begins. And it came to pass when he made an end of speaking unto Saul that the soul of Jonathan was knit with the soul of David and Jonathan loved him as his own soul. Look at that verse in a little more detail in a few minutes. And Saul took him that day and let him go no more to his father's house. And Jonathan and David made a covenant because he loved him as his own soul.  Again, Jonathan is a mighty man of war himself. And he right away just has affinity and just makes this friendship, this covenant with David. Look at verse number five. Now this is interesting because as Jonathan is befriending David and they become these great friends, this is exactly the time when the trouble between Saul and David begins. Look at verse number five. And David went out with us whoever Saul sent him and behaved himself wisely. And Saul set him over the men of war and he was accepted in the sight of all the people, also in the sight of Saul's servants. And it came to pass as they came when David was returned from the slaughter of the Philistines, just think about this for a second.  Imagine the stories back home about David. And this is exactly what's happening. The women came out of the cities of Israel singing and dancing to meet King Saul. And look, Saul was a mighty warrior at this point too. Saul was out, you know, winning battles and he was no slouch himself. With tablets, with joy and with instruments of music. And the women answered one another as they played and said Saul has slain his thousands and David his ten thousands. Uh-oh, we got a problem here. And Saul was very wroth and the saying displeased him and he said they have ascribed unto David ten thousands and to me they have ascribed but thousands. And what can he have more but the kingdom? And Saul eyed David from that day forward. So here we see, you know, just the insecurity of King Saul.  Remember the difference in the Bible? You know, the King James Bible, you know, defines the word envy and jealousy. Look, today envy and jealousy, everyone just uses those two words interchangeably. But that is not true. Jealousy is good, envy is bad. Envy is something where I am upset at the vehicle that Brother Max has. Because it's not mine. So I'm coveting something that somebody else has and I'm envious about it. That's wrong, that's a sin, that's wicked. Galatians chapter five, verse number 26, so just read it for you. It says, let us not be desirous of vain glory. So Saul shouldn't even want glory, provoking one another and being one another. Jealousy is a good thing. Jealousy is actually one of God's names in the Bible. Jealousy is something where you are just protective over something that is yours. God is jealous over you because you belong to him.  A wife can be jealous over her husband because he is hers. It's very simple, all right? But today we're wrecking the English language in so many different levels today. It's ridiculous. But that's a sermon in itself, all right? So this morning, this morning all that is a matter of introduction. This morning I want to look at the life of Jonathan and I want to give you three characteristics of a good friend this morning. Looking at the life of Jonathan. As we go through these characteristics using Jonathan as an example, I want you to think about two things. I want you to think about your friends as I go through these characteristics. And then I want you to think about you as a friend because you hopefully have friends but you are also a friend. So compare these characteristics mainly to yourself and ask yourself what kind of friend am I? The first characteristic is this. A true friend, a good friend will be a loyal friend. And Jonathan was definitely loyal to David. Saul was hunting David from this day forward but Jonathan would not give up on David. No matter what it cost him. No matter what it cost him, whether it cost him the kingdom. See, many people in their lives struggle with loyalty. And it is a bad thing to struggle with loyalty in your life. Loyalty being loyal to something. We're not talking about being loyal to a friend or something that is bad or sinful. The Bible says in Proverbs 27, faithful are the wounds of a friend. Meaning if you have a friend that's getting into sin and all these things, you're not to follow that friend into sin. You're actually supposed to rebuke that friend. Faithful are the wounds of a friend. But the kisses of an enemy, those are the bad things. It's the people that come up and flatter you and say everything that you're doing is great. Those are not your friends. So we're not talking about following being loyal to your friends no matter what kind of sin or what kind of garbage they get into in their life. But that's not the case with Jonathan and David. He gave him his armor.   You need to look the part. In 1 Samuel chapter 2, there's a saying, look the part. In 1 Samuel chapter 19 and chapter number 20, we're going to look at that in just a few minutes. He risks his own life and he's loyal to David at his own peril. He does not give up on David. Struggling with loyalty in your life will mean that you do not have long-term friends. It will mean that you find people that struggle with loyalty in their life and you will see it, friendships are one of them. Their church life is another. You will find people that just can't be loyal to a church or a pastor or whoever and they will just struggle in their church life. They'll struggle with work. These are the type of people that change jobs. Like, you know, we change stocks. They just can't be loyal to any situation in their life. Friendships are a good gauge. Do you have long-term friends? You know, that's one of the benefits. We're going to talk about that tonight, but that's one of the benefits of church life. It's to have long-term life, long friends. And that's one of the benefits that being in a good church that preaches the Bible will give you. We'll talk about that in detail tonight. But look, long-term good friendships. Turn to Genesis chapter 49 in verse number 3. These are people, people that struggle with this are people that have a friend of the month. You know, they change friends. They're just constantly having different friends. They have a church of the month. They have a job of the month. All of that shows instability. Look at Genesis chapter 49, look at verse number 3. When Jacob is blessing his sons, he actually kind of gives a rebuke to Reuben here and he says in verse number 3, he says, Thou art my firstborn, my might in the beginning of my strength, the excellency of my dignity, and the excellency of power. Sounds pretty good. But then look what he says. Unstable as water, thou shalt not excel. Excel in what? He's saying he's unstable. He's not able to be loyal to anything. He's not able to stick with anything. He will not excel at what? He won't excel at anything.  You won't excel at church life. You won't excel with friendships.  That was not Jonathan. Jonathan was loyal to David no matter what kind of situation David was in. Jonathan was loyal to David until the day he died. Turn back to 1 Samuel chapter 18. Look at verse number 1. 1 Samuel chapter 18 in verse number 1. So the first point is this. A good friend will be a loyal friend. A good friend will be a loyal friend. A good friend will not be a fair weather friend. A good friend will not be someone that is your friend as long as you have money. Is your friend as long as things are going well for you and you're fun to hang out with or whatever. No, a good friend will be a loyal friend when you're going through good times and bad times, which brings me to point number 2. True friends will feel your pain. Look at verse number 1 of 1 Samuel chapter 18. Verse number 1 it says, in verse number 1, it repeats this in verse number 3. It says, it came to pass when they made an end of speaking unto Saul that the soul of Jonathan was knit with the soul of David. In verse number 3 it says, he loved him as his own soul. What does this mean? What does this mean? Here's what it means. True friends will feel your pain as if it is their pain. That's what this means. So ask yourself this question. Do you suffer when your friends suffer? That's a good question. That's a good question that we should all ask about our friendships that we have in our lives. Or are you the kind of person, are you the kind of friend that's just kind of like, you don't suffer when your friends suffer, you're kind of like, glad that's not me. That's a good question to ask yourself about your friendships to test you on what kind of friend you are. See, your life will go through tough times. Your family will go through tough times.   You will feel that pain. So the question is, when you have a friend that is going through the same things, does that cause you pain? If it does, it means that your soul is knit to their soul. That your heart is knit to their heart. Good friends are rare. Friends like this are rare. But a good friend's heart and soul will be knit to yours. On the flip side of this, look on the flip side of this, here's a test for your friends. Here's a test now you can think about on people that are your friends. Are your friends happy for you when your times are good? These friends are rare too.  If they're not, you need to take note of that. Because if they're not happy for you in the good times, they're certainly not going to feel your pain in the bad times. It's just another sign. It's an outward sign for you to check your friends. Just like you can check your own type. What kind of friend am I? Does my heart hurt when one of my friends is in trouble, is going through something difficult? Does that, does that matter to me? So it's a good check right here on the kind of friend you are and the kind of friends you have. Go to verse number 4. Look at verse number 4. See, Jonathan was truly happy for David's successes. How do I know? I mean, he was truly happy that he gave him his own garments. He gave him his own armor. He gave him all these things. Jonathan was the prince. Even his father, Saul, rebukes him for this in a couple of chapters. Look at verse number 4. That Jonathan didn't take friendship advice from his dad. Look at verse number 4. And Jonathan stripped himself of the robe. He was a prince. He was the heir to the throne. He was the firstborn son of the first king of Israel. Think about this. He takes his robe and gives it to David.  What does that make David look like now? Now David looks like the heir to the throne. Even his father was like, what are you doing?  But he's not thinking about himself. He's truly happy for David. And he's like, this man's a mighty warrior. He needs to look like one. All he was doing was being happy and thinking about his friend and not himself. So a true friend, a true friend will feel your pain. If you're a good friend, you will feel the pain of your friends. You know, truly be happy for them as well. Here's number three. True friends will sacrifice for you. Jonathan was a great example of a true friend. In verse number four, he sacrifices all his own garments, which, you know, his own prestige. He just gives to David, turned to chapter 19. Just one chapter over. He advocated for his friend. He sacrificed his reputation with his own father for his friend. In verse number one, 1 Samuel chapter 19.  But Jonathan's son delighted much in David and Jonathan told David saying, Saul, my father, seek it to kill thee. So here's that loyalty. Now therefore I pray thee, take heed to thyself until the morning and abide in a secret place and hide thyself. And I will go stand beside my father in the field where thou art. And I will commune with my father of thee and what I see as she'll tell thee. And Jonathan spake good of David unto Saul his father. And said unto him, Let not the king sin against his servant against David, because he had not sinned against thee. And because his works have been to theeward very good. So not only is he warning David showing that loyalty that we already talk about, he's advocating to his father. He's not being coy or secretive to his dad.  He's like, hey, you need to stop doing this. You're sinning. He's trying to get his father to get right. For he did put his life in his hand and slew the Philistine he reminds him. And the Lord wrought a great salvation for all Israel. Thou sawest it and disrejoice. Wherefore then will thou sin against innocent blood to slay David without a cause. And Saul, look at this, Saul hearkened unto the voice of Jonathan and Saul swear as the Lord liveth he shall not be slain. Look, he intervened and he advocated for his friend. He's sacrificing for David. Look at verse 20. It doesn't last long. Saul goes back to wanting to kill David once again. But look at verse 27 of 1 Samuel 20. Now he goes and he advocates for David to his father.  And then Jonathan advocates for David up to the point of risking his own life. Look at verse 27. And it came to pass on the moral which was the second day of the month that David's place was empty. And Saul said unto Jonathan his son wherefore cometh not the son of Jesse to meet neither yesterday nor today. And Jonathan answered Saul, David earnestly asked leave of me to go to Bethlehem. And he said let me go I pray thee for our family have the sacrifice in the city and my brother he hath commanded me to be there and now I have found favor in thine eyes let me get away I pray thee and seek my brethren therefore he cometh not unto the king's table. And Saul's anger was kindled against Jonathan and he said unto him thou son of the perverse rebellious woman do not I know that thou hast chosen the son of Jesse to thine own confusion and unto the confusion of thy mother's nakedness.   It's basically what he's saying to Jonathan. And he's rebuking Jonathan because Jonathan is protecting David. And then Saul brings up what many of us might have thought when he gave away his sword and he gave away his robe and he gave away his cloak to David. He says for as long as the son of Jesse liveth on the ground thou shalt not be established nor thy kingdom.  He's saying you're not going to be king as long as he's alive. Why would you not want him dead? Is what Saul is saying? And Jonathan answered, Saul's father and said unto him wherefore shall he be slain? What hath he done? It didn't matter to Jonathan what he could possibly get from David's death. He was loyal and he was just sacrificing again and again for David. And look, he was sacrificing even his own kingdom at this point. Of course we know that God chose David already to be king but the point is, is from a secular point of view Jonathan is literally giving up his kingdom to David. Look at verse number 33. And Saul cast a javelin at him to smite him.  So Jonathan has risked his life for his friend. Whereby Jonathan knew that it was determined of his father to slay David. So Jonathan, here's another proof of that friendship of his. How Jonathan's heart hurt when David hurt. Look at verse number 34. So Jonathan arose from the table in fierce anger and did eat no meat the second day of the month for he was grieved for David because his father had done him shame. He's hurting for his friend. David is running. He's hiding. He's suffering. He's in pain. And so is Jonathan. Why? Because he's a good friend. That's why. Turn to 1st Samuel chapter 31. 1st Samuel chapter 31. 1st Samuel chapter 31.  Jonathan dies early in 1st Samuel chapter 31. The Bible says in verse number 1 of 1st Samuel chapter 31 that this great friend to David dies with his father. Now the Philistines fought against Israel and the men of Israel fled from before the Philistines and fell down slain in Mount Gilbola. And the Philistines followed hard upon Saul and upon his sons and the Philistines slew Jonathan and Abinadab and Melchishua, Saul's sons. So here Saul's sons suffer for the judgment that was coming upon Saul. That's kind of a sad ending to Jonathan's life because we see that he was an honorable friend. He was a good friend to David. He was loyal to David. He sacrificed for David. But just a side point here. Children will suffer or benefit from the decisions of their parents. That's why David says in Psalm chapter 16 in verse number 6. He says, The lines have fallen in pleasant places. Yea, I have a goodly heritage. David is proclaiming in Psalm 16 verse number 6 the opposite of what Saul gave to Jonathan. David is proclaiming the goodly heritage that he got from Jesse his father in Psalm chapter 16 in verse number 6.  Is that children will benefit from our lives or they will suffer from the decisions that we make in our lives. And that becomes the end of Jonathan. Now you can say it seems like a one-sided friendship between David and Jonathan. It seems like a one-sided friendship. Should friendships be one-sided? No, they should not. One-sided friendships where one friend is just constantly sacrificing, constantly being loyal, constantly looking out for and constantly just feeling the pain of one friend. Those types of relationships, those types of friendships, they exist. But they usually don't exist for long if they're one-sided. You say, well, wasn't this a one-sided friendship? Because it was just Jonathan that we saw was doing all these great things as a friend. Well, turn to 2 Samuel chapter 9. Turn to 2 Samuel chapter 9 and we'll see that this was not a one-sided friendship. Turn to 2 Samuel chapter 9 and look at verse number 1. 2 Samuel chapter 9, verse number 1. After David becomes king, now David is ruling the kingdom. Look at verse number 1. David said, is there yet any that is left of the house of Saul that I may show him kindness? Why? For Jonathan's sake. Look at verse number 2. So David is looking for anybody that is related to Saul. Look, David can't do anything after 1 Samuel chapter 31. He can't do anything for Jonathan. David finally gets out of his hole. He gets out of his cave. He's ruling the kingdom at this point and he says, now I can do something for my friend. It just happens that his friend is dead. So he says, hey, is anyone left of his entire family that I may show kindness? Why? For my friend's sake. Look at verse number 2. And there was of the house of Saul a servant whose name was Zeba and when they had called him unto David art thou Zeba and he said, thy servant is he. And the king said, is there not yet any of the house of Saul that I may show the kindness of God unto him? And Zeba said unto the king, Jonathan hath yet a son which is lame on his feet. So here he tells him that your friend has a boy. He has a son who's, you know, he's disabled. He's lame on his feet. He doesn't say why and says the king said unto him, and Zeba said unto the king, behold, he is in the house of Maker, the son of Emil in load bar. King David sent and fetched him out of the house of Maker, the son of Emil from load bar. Now in Mephibosheth, the son of Jonathan, the son of Saul, was come unto David. He fell on his face and did reverence. And David said Mephibosheth and he answered, behold, thy servant. And look at this. And David said unto him, fear not, for I will surely show thee kindness for Jonathan thy father's sake and will restore thee all the land of Saul thy father, and thou shall eat bread at my table continually. He says you're going to inherit everything that even Saul owned is going to be yours. He says I will take care of you and make sure that you are taken care of for the rest of your life. So it was not a one-sided friendship. David found a way to be a friend back to Jonathan even after he was dead. So this morning, you should look at your friendships. If you have friendships in your life and you say, you know, these friendships, I got a lot of friends and you know, it doesn't cost me anything. I've got a lot of friends. That just means that people do things for me. That just means that I got a lot of people that helped me out and do things and whenever I need somebody to help me with something on my house, I've always got people there. Look, that's not friendship. That's brotherly love that someone is showing you. Friendships, true friendships will cost you and that's the important point that you need to take away this morning or if they don't cost you, you are not a friend. You may have people that are friendly to you but if it doesn't cost you anything you are not a friend. You aren't a friend back. Look at Proverbs chapter 18. Look at Proverbs chapter 18. Look at verse number 24. Proverbs chapter 18. Look at verse number 24. The Bible says in Proverbs 18 24 it says a man that hath friends if this is you, it says what? Must show himself friendly and there's a friend that sticketh closer than a brother. So to be a friend you must show yourself friendly and you must sticketh close meaning you have to actually do things to be a friend. The Bible here in Proverbs chapter 18 in verse number 24 is saying if you want to actually be a friend and not just have friends look it's saying a man that hath friends is like you should do this back to your friends. You should do things. You should take action towards your friends. Look at John chapter 15. See there's a spectrum here. We like spectrums. There's a spectrum of friendships.  There's a spectrum of glad it's not me. That's the wrong side of the spectrum. And then there's this spectrum in John chapter 15. Look at John chapter 15 verse number 13. So we get the glad it's not me friend. Somebody's going through a terrible time. A friend of yours is going through a terrible time and the only thing that you can think about or the only thing that you feel is glad that's not happening to me. That's the spectrum we want to stay away from. Here's where God wants you. Look at verse number 13. It says greater love hath no man than this that a man lay down his life for his friends. Here's what a true friend says. A friend is in trouble and he's in trouble to the point where he could die. A true friend says all die for you.  You're like that's crazy. That's extreme. Look there's all kinds of stories about this throughout history. I don't know if I'm like too nerdy in my thought process or thinking about the jobs that I've done in the past and things like that, but when I think about this idea of just a man laying down his life so other people could live, I think about Chernobyl. You remember that? I think about this horrible accident that happened at this nuclear power plant in I think it was Belarus, actually not Russia. But it was in this ex-Russian republic of Belarus and this horrible incident happened. This reactor exploded. There was radiation everywhere. One of the units just literally exploded. And there was a problem where this pool of water was filling up. It was filling up with this radioactive water and it was going to flow into this other area that was going to cause the other three units to explode in the same way that the first one exploded. And somebody had to go through this water to shut these valves to stop this from happening. And three people, three men, they volunteered to do this. It was certain death. But they volunteered. They stood up and they volunteered and I think it was the Soviet Union at the time. The Soviet Union was like, we'll take care of your families and all this. But I mean, even though the Soviet Union, Communist Russia, I get it, these three men were incredibly brave people who just stood up and said, we will give our lives so other people can live. And what did they do? They waited through the water. After much trouble and much time in the water, they shut the valves, they stopped the disaster, and they died. But they saved many, many people in doing so. Look, the reason stories like the one I just told you are so extraordinary is because stories like that are rare. Stories where men will just stand up and just face certain death so other people can live. Albert Vanderbilt. There was the Lusitania, the ship. It was hit by a Russian U-boat in 1915. And this incredibly rich billionaire was on the ship. He gave his life jacket to other people and he gave his spot in the lifeboats and just helped load people in the lifeboats and never found his body. But I mean, that is the opposite spectrum of glad it's not happening to me, is literally laying down your life for your friends. Look, those three people at Chernobyl, they were being friends, true friends, as the Bible defines it. Vanderbilt was a true friend to those people on that boat. So the question is, how good of a friend are you? That's the question this morning. Ultimately, turn to John chapter 3. Ultimately, do you love your friends? This is really the question, because that's how the Bible defines Jonathan, his actions towards David. It's like he loved him as his own soul. And then the Bible defines what true actual love is by the actions that Jonathan took throughout his life, including dying early for his friend David. So if you love your friends, you will be loyal to them. You will feel pain and joy with them. And you will sacrifice for them. I mean, ultimately the biggest example of this is Jesus Christ. Look at John chapter 3 and verse 16. People know this verse. For God so loved the world, because he wrote the Bible that says, I love you, I love you all. That's what people think love is today. People think love, you know, this is a problem people will have in their marriage. Whereas they go, I love my wife. I love my wife, but you do nothing to show her. Because love is not words. Love is not you having some butterfly feeling in your stomach. This is what young people need to understand. Love is action. Doing something. That's what Jonathan shows us. Ultimately, I thank God that that's what Jesus Christ showed us. That God didn't say, hey, love you all.  Love you all. Hope you can be perfect.  Love, and then you got the other sick satanic side of it that says love is lust today. Oh, love. No, that's abomination. Love is action. Love is action. And I thank God that he knows what love actually means. For God so loved the world that he gave his only begotten son. That's what that meant. How did he do love us? He gave us his son. That whosoever what? Believe it in him should not perish but have everlasting life. So the question is this morning, is it a one-sided relationship between you and God? Do you love the God that loved you? Because he saved you without your works. He saved you without any action coming from you. He saved you. God showed his love. He commended his love toward us while we were yet sinners. He didn't say, hey, clean it up. Clean it up.  No, he showed his love toward us. He commended his love toward us while we were yet sinners. So the question is, do you love God? That's why in John chapter 14 of verse 15 he says, if he loved me, so there's no question about whether or not God loved you. The question is, do you love God? Do you show action towards God? He already saved you. You're saved no matter what you do. But if you love me, keep my commandments.  Follow the Bible. So you see, Jonathan, he's an example of a great friend. We should be great friends to those around us. We should have two-way friendships where your friends do things for you and you do things back to them. That's showing that love that we're talking about here. But hopefully, but ultimately, look at this, folks. The type of friend that you are will really be reflected in the type of Christian that you are. Because your friendships towards people on this earth, your brothers and sisters in Christ is really just an example of the ultimate love that you have for the Lord.  God loved them, just like he loved the Christian that's actually showing love back towards God. So look, our idea of friendship as it comes from us will define our relationship with the Lord who saved us. Don't make it one-sided. Let's bow our heads and have a word of prayer.


Hi guys, this is Dr. Ahmed Ergin. Today I'm going to answer a question that sometimes comes to me from even non-diabetics So why do diabetics take insulin? So it's an easy answer, right? But before that, let me introduce myself I'm Dr. Ergin. I'm a diabetes expert. I see diabetes every day in my clinic And I am happy to answer your questions here in this platform Not necessarily personal questions, but definitely journal questions will take and I'm trying to answer all the questions in these videos now Why diabetics sometimes need insulin? If you have type 1 diabetes, your body basically gives up making insulin So you have no choice but to take insulin. Now most people like they will start taking insulin at age 2-3 And they take insulin entirely their life and as long as they know what they're doing, they have no problem whatsoever Now why type 2 diabetics end up taking insulin? Why do they become insulin dependent? Now most of the time they don't actually need to take insulin But they end up being on insulin because sometimes doctors don't consider other treatments before they jump to insulin The reason though, the bottom line is your body is just not able to keep up with the needs Which is keeping your blood sugar down So if you're like doing everything you can, your doctor has done everything they can and your blood sugars are still high in the morning Your blood sugars are still high after you eat. That means that your body is just not able to keep up with it Now I'm not saying here that every time you see that your blood sugar is high You need to jump on the insulin What I'm saying is after you try everything By the way, trying everything is a subjective thing So you have to really probably see an endocrinologist and consider all your options before you jump to an insulin Because there are a lot of options other than insulin and in my clinic It's not uncommon actually a few times a day people come to me on insulin Within a couple of weeks we take them off the insulin because we offer them other options We adjust their lifestyle.   There are a lot of ways you can break it But if you are not able to break your insulin resistance and you tried everything Unfortunately, you're looking for insulin. That's why sometimes even type 2 diabetic patients end up taking insulin So sometimes I see a lot of patients like who take insulin and they don't care They say, you know, just give me the insulin because I don't want to change anything in my lifestyle But that's not always the best thing because it's going to make you gain weight It's going to cause sometimes low blood sugars and most of all it's a painful thing I mean you have to keep doing it not that it's painful to inject yourself But trying to keep insulin pens around or using insulin pump, etc Is not always the most fun thing to do So I always encourage my patients to adjust to your lifestyle Follow our instructions so we can keep them off the insulin Well, I hope that helps. We will see you in the next video guys


You can apply for article processing charges, or APCs, from Union's Helsinki Centralized APC Fund to publish in open access journals, but the fund is not available for publishing in hybrid journals. Sometimes it can, however, be difficult to tell if the journal is a hybrid or an open access journal, and this video shows some ways to check that. The directory of open access journals, DOAGE, is a database which currently in 2022 lists over 18,000 open access journals, of which about 5,000 charge APCs. So most open access journals are free for both readers and authors. DOAGE also shows the amount of APCs of journals. If the journal is listed in DOAGE, it is definitely an open access journal. But not all open access journals are included in DOAGE, which means that if you can't find a journal there, it doesn't necessarily mean that it's a subscription or a hybrid journal. In any case, open access journals tend to be fairly unambiguous about their open access status, whether they belong to DOAGE or not. If you can't find an answer this way, you can check the journal website and browse the contents of any issue of the journal. If some articles are open access and some are not, the journal is most likely a hybrid journal. What might cause confusion is that if the journal is subscribed by the library and the user is currently in Union's network locally or via VPN, all articles are available to read. An open access logo or a Creative Commons license is a sign if an article is open access and a free or full access label just indicates that the journal is part of Union's subscriptions. There are many reasons why the hybrid model is problematic, which is why hybrid journals don't often use that term themselves. Subscription journals might just tell you about their open access options, which means that you can pay for single articles to be opened, which is the hybrid model. If you can't find the answer to whether a journal is an open access or a hybrid journal, you can always contact the library for help.