تبطه آدك الأيام فتا الأسل الثاني أمر الله بالإجتماعي في الدين ونهى عن انتفرق فيه اليوم إن شاء الله يتعالى we're gonna go into the second asal the second asal in our great book شرحوا أصول الستة لشيخ الإسلام محمد بن عبد الوهاب the second asal the second fundamental thing that is needed is that the person needs to know that it's obligatory وجوب it is obligatory الاجتماعي على الحق pay attention وجوب الاجتماعي على الحق that it's obligatory to unite upon the حق ونهى that it's prohibited عن التفرق فيه and that it's prohibited to differ in the حق this is a asal which is very important the sheikh said أمر الله الله ordered this is what الله سبحانه وتعالى ordered us what بن اجتماعي to unite في الدين in the religion ونهى عن التفرق فيه and that Allah has prohibited us of what to differ within the religion الله سبحانه وتعالى now what I'm going to do is I'm going to mention to you أسباب الإختلاف والتفرق what are the things that cause differing and to become groups and sects what causes it before I go into the speech of I'm going to mention that and then I'm also going to mention another point after this what are the things that cause people to differ to be of groups and sects and every single person to have his own banner his own flag and to say where called this and you guys are called that and you're called that and that's our names what causes it the first one is اتباع الهواء following your whims and desires if every single person follows his own whims and desires whims and desires does not unite the people because every single person his desires is different to the other person he desires something different to the other person ولذلك الله تبارقة عليه سلم القرآن هو الذي أنزل عليك الكتاب منه آيات محكمات هون أم الكتاب وأخر متشابهات فأم الذين في قلوبهم زيغ فيتبعون ما تشابه منه بتغاء الفتنة وبتغاء تأويلي الله سبحانه وتعالى فأم الذين في قلوبهم زيغ those who have in their hearts deviation whims and desires overcame them what do they follow they follow the verses which are ambiguous because they have desires in themselves they won't go to the verses which are محكم the clicker verses they will bring you آيات which ambiguous are unclear what does Allah mean by this verse it has to be explained with another آية because he has whims and desires filled in his heart so he will force you to go to these verses and that is what makes people become groups and sects the people become what فراقن sects by following their whims and desires وبيمور وبيمور فارقة ديني and differing with the religion until they become what and they become different نحل and sects the second one brothers is the second one is الجهل ignorance ignorance what does it cause brothers ignorance is the things that causes الاختلاف والتفرق these people to differ and to be different ignorance causes it من أسباب الجهلي the causes of التفرق والاختلاف is الجهل وبيدين الله when the people are ignorant of the religion of Allah والكلام في دين الله بلا علم and the person starts speaking about the religion of Allah without knowledge he has no understanding of the deem ولي ذلك our messenger صلى الله عليه وسلم he said in the hadith of عبد الله بن عمر بن العاص رضي الله تعالى عنهما may Allah be pleased with عبد الله and may Allah be pleased with his father عمر بن العاص this hadith is narrated by Imam al-Bukhari and Muslim in their both both of them in their authentic book في صحي حيهما that the prophet صلى الله عليه وسلم he said إن الله لا يقبض العلم الله does not take knowledge انتزا عن ينتزيعه من الناس الله does not take knowledge which he takes away from the people الله does not take and lift the knowledge from the people and take it away from their hearts he doesn't do that how does Allah take knowledge ولكن يقبض العلم بقبض العلماء الله takes knowledge by taking the people of knowledge الله تعالى he takes the knowledge by taking its people who are carrying it حتى إذا لم يبقى عالم until there is no scholar left اتخذ الناس رؤوسا جهالا and based on that the people they take the ignorant ones as their leaders that's what they do they start pointing towards an ignorant individual and they say شيخنا our teacher so and so فسؤلو and then the ignorant one is questioned فأفتو بغير علم فضلو واضلو they give fatwa the ignorant one gives a fatwa and what happens without knowledge فضلو he misguides the people واضلو and they misguide themselves he misguides himself and he misguides others ولذلك I think ربيع ابن عبد الرحمن ربيعة الرأي امام ماليك's teacher امام ماليك's teacher and I believe it was him ربيع ابن عبد الرحمن ربيعة الرأي he cried one day and they said to him ماليك's teacher was making you cry pay attention to this speech they said that today on the Earth there has come people who are giving fatwa هذا هو ربيع إماماليكس تيشة في ذلك time there were people giving fatwa passing rules of Allah's religion سبحانه وتعالى without knowledge without knowledge and without understanding of the book of Allah who سبحانه وتعالى جهل and then you see subhan Allah people who are giving da'wa who are saying we're calling to the religion of Allah they don't even know the mbaadi of the religion the beginning, the fundamental matters of the religion they don't know it and they are out there giving what الدعوة إلى الله تبارك وتعالى they are calling to the deen of Allah they are calling to what دعاات call us to the religion of الله سبحانه وتعالى and what does that call brothers it calls is الاختلاف والتفرق و لذلك the salaf some of them used to say لو سكت من لا يعلم if he was to be silent the one who doesn't know if he was silent and he closed his mouth the one who doesn't know what would have happened لقلت الخلاف the dispute and the خلاف would be little if the jahil was quiet and he didn't talk and he let the scholars talk and he left it to the scholars then the خلاف would be little but because everybody is contributing his thoughts what do you think what do you think it has caused what it has caused hundreds of views views of who like him لا جهال ignorant people and so basically the people then they say the scholars differed in this issue what scholars differed in this issue there's no scholars نعم so الجهل ignorance of the religion of Allah اخواني is من اسباب الاختلاف والتفرق in the religion of Allah one of the things also be brothers and sisters is that causes الاختلاف في الدين والتفرق فيه is what الاعتماد على المعقول if a person relies on their intellect in taking the عقيدة في اخذ العقيدة when taking عقيدة the person relies on his intellect و ترك الاستدلالي بالمنقول and the person leaves off what and the person leaves off looking for the textual evidences he doesn't rely on the textual evidences he relies on logic intellects of people these are the things that cause what why would it cause it because they are the views of people and the way that people's brains work are they different or not they are different there has to be something that governs them all what is it شالله تعالي I'm going to speak about it later بإذن الله الكريم the things that govern us اخواني is الكتاب و سمنا we're going to speak about that in the other point that I want to speak about شالله تعالي also brothers من اسباب الاختلاف والتفرق في الدين one of the things brothers one of the things brothers that causes الاختلاف والتفرق في الدين is what طعنوا في علماء السنة criticizing slandering the scholars of the sunnah و مدحو آهل الأهواء والبداعي and praising the innovators and the people of the winds of desires a person who is مبتدع who is an innovator who calls to innovation you praise him and you are giving him a position and you slander who you slander the علماء the hurras of the sharia the people are standing to protect the sharia they are criticized and they slandered and أهل البداعواء they are praised these are from the things that are what من اسباب الاختلاف والتفرق في الدين it is from the things brothers that cause what it causes the ummah to disunite and to differ people who are deviating the ummah from the straight path brothers and sisters الله تبارك وتعالى based on the hadith ابن ماجه نريتر ابن ماجه نريتر on the authority of عوف ابن مالك he is عوف ابن مالك الأشجع رضي الله تعالى عنه he said I heard the messenger صلى الله عليه وسلم say I heard the messenger صلى الله عليه وسلم say the messenger صلى الله عليه وسلم he said افترقت اليهود على إحدى وسبعين فرقه the jews they broke into 71 sects فوحدة في الجنة وسبعين في النار 70 of them in the house fire and one of them in the paradise وفترقت النصار وفترقت النصار the Christians they broke into harmony على ثمتيني وسبعين فرقه 72 فإحدى وسبعين في النار harmony 71 of them in the house fire ووحدة في الجنة and one is entering jannah والذي نفس محمد محمد بيده the prophet then said I swear by the lord in which Muhammad me myself the prophet of Allah whose hand I swear by the one whose hand my soul is in I swear by him الله تباركه تعالى do we believe the prophet without him without him having to say that yes we already believe him imagine if he said this he said this we would have taken it from him even if he didn't say this statement that I swear by the one who my soul is in his hand we would have taken it from him صلى الله عليه وسلم because he is صادق المصدوق but imagine if he said it it would become even what it would be more serious to us he said that I swear by the lord my soul is in his hand لتفتريقانا they will break into this is known as توكيد they will break him and they will break and they will break and they will sect my umma will do على ثلاثين وسبعين فيرقاه 73 they will turn into 73 sects my umma واحدة في الجنة only one is in jannah وثنتان وسبعون في النار and 72 are in the house fire قيل يا رسول الله or messenger of Allah who are the same sect who are the one group that is going to enter jannah the messenger said الجماعة الجماعة is what الجماعة is the group there is another another narration tell me the narration narrated it that the messenger of Allah that the messenger of Allah explained who the جماعة is who is this جماعة the prophet in the other narration what did he say ماءانا عليه اليومة واصحابي anyone who is upon that which I and my companions are upon today anyone who is upon that which I and my companions are what upon brothers and sisters I want to ask you that some of the scholars some scholars weakened it or it was weakened the narration ماءانا عليه اليومة واصحابي some weakened it that narration is strengthened by the narration of الجماعة it's a Shahid for the other narration it strengthens it why because الجماعة at that time the prophet is companions was there any other جماعة لا so ماءانا عليه اليومة واصحابي and الجماعة both mean the same is a تفسير and a bayan of the other narration and it could be a Shahid for it brothers I want to ask you this question did the prophet said more than one group is going to go to جنة or one it's only one it's only one sect and they are the safe sect الطائفة المنصورة so anyone who tells you اخي this group and that group and us we all have different names but don't worry we all get into جنة there can only be one who is going to جنة from the 73 we know only one is entering جنة امام مصفارين رحم الله in his لوامع الأنوار he did a mistake here and he goes clearly against the hadith of the prophet he even himself رحم الله تراقظ he contradicted himself on the issue of saying that the safe sect هو he said it is a شاعرة and the maturidia اهل الحديث how could it be when the prophet is saying it is what if you ask a شاعرة today are you and the maturidia they will say both of us but the prophet said what it is one it can only be what one group now it brings me to the next point إن شاء الله تعالى our brothers and sisters we today find جماعات احزاب we have sects groups names this is called حزب التحرير this is called اخوان المسلمين this is called جماعات التبليغ and the list goes on all of them are saying we are working to the establishing of Islam on this earth and we are all what we are working to what we are all working to the same it's just that everyone is taking a different approach everyone is taking a different means first of all based on this حديث we only know one is going to enter جنة only one group is the طائفة المسورة of the safe sect now we have to ask ourselves all of these groups that we find today and those are not the only groups there are more like in these this is على سبيل كمثيل this is just an example of those who are out there right now with these points you will realize the answer of this question because it needs to be explained in details the first thing that we will have to ask ourselves is when we dispute one another and we differ on a matter where do we go back to if we differ on a matter and we have different views on a matter what is the مرجعية where is the sauce that we were ordered to go back to based on the آية الله تعالى فإن تنازعتم في شيء فردوه إلى الله والرسولي إن كنتم تؤمنون بالله وليوم الأخير if you guys dispute one another in a matter bring it back to who bring it back to Allah and his messenger if you are those who believe in Allah in the day of judgment سورة النساء آية 50 59 so that آية Allah tells us to bring our dispute back to who تكتابا لا and the sunnah also الله تعالى تعالى سورة النساء آية 83 الله said وإذا جاءهم أمر من الأمن أو الخوف أذاعوا به ولو ردوه إلى الرسول وإلى أولي الأمر منهم لعلمه الذين استمبطون منهم الله says if a matter of good came to them or a matter of fear came to them they will they do إذاع they will announce it ولو ردوه if only they brought a matter back to where if they were to bring it back to إلى الرسول to the messenger وإلى أولي الأمر منهم and if they were to bring it back to the people of knowledge the people who have authority over them الله says العلمه الذين استمبطون منهم the messenger صلى الله عليه وسلم also said in the hadith الإمام المندر ناري ترغيب ترغيب خلبان authenticated I had left you guys with what I have left with you ما إنعطة سمتون something if you guys hold on to فلنت ضلوا أبدن you will never be misguided I have left with you something that if you guys hold on to it after my death you will never be misguided I have left something like that for you the prophet tells us what it is كتاب الله وصوصونة نبيه and the prophetic tradition of the لذا إذا كنا نرى ما الله قلت right now and what the Prophet صلى الله عليه وسلم what was it that they told us they told us أن نرود كل خصومة in every argument and every dispute and every differing that we have we bring it and we bring it back to him إلا الله to Allah and ورسوله his messenger to bring it back to Allah and his messenger if we do that what will happen brothers and sisters وحي نقل تزول الخصومة our dispute and our argument will what it will uplift from us إن شاء الله و تعالى and we will find our solution there and the ayat that tell us to do that are immense and that's غيضون من فيضن that's just a dip from the ocean it's not all of it now the second point that we need to really we need to understand this now that we've understood the Kitab and the Sunnah is our source the second question is that who's understanding are we going to base it on this Kitab and the Sunnah that we have amongst ourselves right now who's understanding are we going to base it on who's understanding are we going to base it on we're going to base the Kitab and the Sunnah based on that which الله tells us to base the understanding on Allah has told us already who we need to base هل تفهمت هذا؟ القرآن في السنة الله تباركه تعالى يسان صورة النساء 115 الله يقول ومن يشاقق الرسولة anyone who goes against a messenger صلى الله عليه وسلم من بعد ما تبين له الهداة after clear evidence has come to him ويتبع ويتبع غير سبيل المؤمنين other than the path of the believers he follows the path different to the path of the believers الله says wherever path you have treaded on and that you've taken الله will let you be on that path of destruction and then what will happen ونصليه جهنم and the hellfire will be your abode and Allah then says what an evil place for you to stay the hellfire what a bad place for you to be so when this ayah came down who are the believers at that time who were the believers of that time ويتبع غير السبيل المؤمنين who had that statement who had that name مؤمنين us we weren't even there the believers of that time were the sahabas رضوان الله عليكم عين so anybody who follows a path other than the path of the believers and it doesn't mean it's only the sahabas but it means from them first they are what اولوية الدخول they're the first ones who entered the verse because it came down when they were there also الله تبارك واتعاله he set us in the ayah فإن آمنوا if they believe بمثلي ما آمنتم به الله is saying in this ayah if they believe the way you guys have believed فقد يتدو they are guided وإن تولو if they turn away from you Muhammad صلى الله عليه وسلم and your companions if they turn away from it they are upon a deviated path so الشقاق يميز البعضو that you are distant from what من هجو رسول الله صلى الله عليه وسلم وأصحابه you are far from the path of the messengers صلى الله عليه وسلم and his companions رضوان الله عليكم عين in the deen in this religion the third point that we need to realize brothers is that we need to ask ourselves is are we allowed to to believe something and then look for the evidence or do we look for the evidence first and then we believe it based on the evidence that comes to us الله تبارك وتعالى answers that for us سبحانه وتعالى in صورة محمد ayah 19 الله تبارك وتعالى he says to us فعلم no first of all أنه لا إله إلا الله وستغفلي ذنبك الله says to us no that there is none worthy of worship except Allah and then once you have the knowledge وستغفلي ذنبك ask Allah for forgiveness for your shortcomings so what has Allah put first Allah has put knowledge first إمام البخاري رحمه الله in his صحيح his authentic book he chapted a bab and he called it what باب the chapter which is what العلم قبل القول والعمن knowledge precedes speech and action وإمام البخاري's chapterings brothers بارك الله فيكم it's not an ordinary chapterings the chapterings of بخاري the علمات they say فق البخاري يق إمام البخاري is thick his rulings that he is extracting are based on his chapterings when he chapters رحمه الله so now إمام البخاري in that chaptering he is trying to say to us that this is how it should be that knowledge should precede any action or speech that you do don't call the people to the religion of Allah don't preach if you don't have knowledge don't act if you don't have knowledge don't believe if you don't have knowledge have knowledge of it why because knowledge precedes it so you have a belief of a system and you believe battle and then you're looking for evidences are you going to accept it you're not going to accept it and that is mean علمات إهل البداع signs of the people of innovation they believe something first and then they go out of their way to look for what to look for the evidences so you look for the evidences from the Kitab and the Sunnah and the understanding of the Salaf of this Ummah before you start believing in it before you what before you start to believe in it ولي داركة the scholars they say that this what do they do يعتقدون ثم يستدلون فيضلون they believe then they look for the evidences and then they become misguided هل سنة أوت يستدلون ثم يعتقدون فيهتدون they look for that they look for the guidance first then they believe in the evidences that came to them from the Kitab and the Sunnah and on the understanding of the Salaf of this Ummah based on that they start to believe now based on that they start to believe good did the Shari'a part number 4 did the Shari'a place for us a way to call to the path of Allah did our Shari'a did it place for us a methodology to call to the path of Allah of course it did صورة النحل ay 125 Allah says ادعو call to الى سبيل ربك بالحكمة والموعظة الحسنة call to the path of your Lord ادعو الى سبيل ربك call to the path of your Lord الله تبارك وتعالى with wisdom والموعظة الحسنة and with good reminders معوظة الحسنة call to Allah تبارك وتعالى he said تبارك وتعالى before I bring the ayah ابن جليل الطابر he said ادعو الى سبيل ربك بالحكمة والموعظة الحسنة what does it mean ابن جليل الطابر he said هو ما أنزله عليه من الكتاب والسنة call to the path of Allah based on what ابن جليل said it is that which Allah has sent from the book and the sunnah the Quran and the sunnah when you are calling you have the Quran and the sunnah with you he said قال الله قال رسوله صلى الله عليه وسلم and this is the understanding of the Salaf of this ummah how they understood it good very good so the da'wah our shari'ah has placed for us based on the ayah what we need to call to the people what we call to the people too the Kitab and the sunnah on what understanding my understanding the 21st century understanding everyone open the mushaf and try to see what you get out of it and based on that we make our da'wah or everyone let's revise or let's do a new manual guide for da'wah is that what we're going to do لا this is a manhaj you have to follow I will message you صلى الله عليه وسلم وَدِلْهِسَيْ وَأَنَّ هَذَا سِرَاطِ مُسْتَقِيمًا فَتَّبِعُوهُ وَلا تَتَّبِعُ السُبُلَ فَتَفَرَّقَ بِكُمْ عَنْ سَبِيلِ ذَالِكُمْ وَصَّاكُمْ بِهِلَ عَلَّكُمْ تَتَّقُونَ that is my path وَنَّ هَذَا سِرَاطِ this is my path my path in terms of speech my path in terms of action my path in terms of belief my path in terms of how I call the people to وَانَّ هَذَا سِرَاطِ مُسْتَقِيمًا my path is straight it's مُستَقِيمًا فَتَّبِعُوهُ who follow that path وَلا تَتَّبِعُ السُبُلَ don't follow a group don't follow a group what will happen to you وَلا تَتَّبِعُ السُبُلَ فَتَّفَرَّقَ بِكُمْ عَنْ سَبِيلِ it will deviate you from the straight path it will deviate you from what the path of the messenger صلى الله عليه وسلم when the prophet recited the ayah he not only did he say it to the sahabahs but the messenger took a twig عليه صلى الله عليه وسلم بيسان حديث عبدالله من المسعود the prophet took a twig خطة لنا رسول الله صلى الله عليه وسلم خطة مُستقيمًا على الأرض the prophet took a twig he made a straight line on the path and on the sides of it he made lines that came out of it and then the messenger recited the ayah وَأَنَّ هَذَا صِرَاطِ مُستَقِيمًا فَتَّبِعُوا وَلا تَتَّبِعُوا السُبُلَ سُبُلَ فَتَّفَرَّقَ بِكُمْ عَنْ سَبِيلِ don't follow these path are deviated from my straight path don't follow it what will it do it will deviate you it will corrupt your mind and now we find people who made the da'wah if Islam is going to lift his head أخي be part of be part of those who do or participate in parliamentary elections elect that's how Islam is going to lift its head did the messenger do that عليه الصلاة والسلام was his da'wah in Makkah be part of أهل الشورa of Quraish or to be part of sit down with Quraish and to be part of their committee in order for Islam to gain a government is that what the messenger عليه الصلاة والسلام did ever done he never done it عليه الصلاة والسلام so brothers the way it is is that that the sharia had placed the da'wah should be which is الكتاب والسلح بفهم سلاة في الأمة


If you think about the Middle East right now, think about all the conflicts in the Middle East right now. We've got Hamas. Hamas and the Palestinians attacking Israel and Israel defending itself. Hamas could not attack Israel without Iranian funding, without Iranian arming, and without Iranian, actual Iranian support in terms of even training on how to use drones, electronic warfare, that made October 7th possible. Hamas and the whole Palestinian war against Israel at this point is pretty dead without dramatic Iranian support. And there's no question that the Iranians were part of the planning and the decision to execute on October 7th. If you go further north to the Israeli-Lebanon border, which is could any day turn into a ground war, but right now is just each side bombing each other in a tit-for-tat type situation. Hezbollah is a branch of the Iranian, basically revolutionary God. Hezbollah was founded by the Iranian Secret Service. It was founded by Iranians. It's been funded and receives its marching orders to a large extent from Iran. It leads, indeed it is the largest and most militarily active or has been of all and oldest because it goes back, it goes back to the 1980s, oldest of Iran's puppets. And it is on the verge of war with Israel. If you look at Syria, which has been involved in a civil war, God, I can't remember when it started, but for the last decade or so, 10 years plus, Syria is a country that receives the regime, which was almost overthrown by various elements, some you could argue worse than the regime, some significantly better than regime. It's only ally who's basically been Iran. Iran has been at well, Russia ultimately, but originally only Iran. Iran has been at the center of that conflict. They are funded and again supported with troops and a variety of other mechanisms. The Assad regime in Syria have allowed him to kill his own people, to destroy his own country, and ultimately to beat back most of the insurgents who were fighting against him. Iran has been instrumental in destabilizing Iraq since the United States invaded. The Shiites, who are the majority in Iraq, could have used the opportunity of Saddam Hussein's fall to really establish a relatively free country and one run by the Shiite majority or at least in a parliamentary system, a country that could be relatively rich because of its massive quantity of oil that exists in Iraq. And instead, the Iranians have done everything to turn it into a satellite state. And if not, when the Iraqis resist becoming a satellite state to ferment whatever instability and whatever violence they can, and they've done that from the beginning of the U.S. invasion and they continue to do that today. Part of that, the American forces in Iraq that are basically that train the Iraqi army and to continue the fight against elements of al-Qaeda and particularly ISIS in Iraq and in Syria, those American bases are being attacked by Iranian linked militias. That's what they call them anyway. Really for well over 10 years now, well into going back, really they were attacked during the Bush administration and the Obama administration, Trump and Biden. So all the kind of violence going on in Iraq and in Syria to logist that Iran has its hands in it. The final area of conflict the one has to look at is the Houthis in Yemen. The Houthis in Yemen are again a puppet, funded, supported, trained, armed by the Iranian regime. They are also, in this case, Shiite. The only one of these parties that's not Shiite is Hamas, but everybody else is Shiite, the same sect of Islam as Iran. And they have been devastating Yemen with the civil war for many, many years and now, of course, threatening the sea lanes in the Red Sea and up into the Suez Canal. In every conflict in the Middle East, Iran isn't just dabbling, isn't just helping a little bit here and there. Iran is at the core of it. Iran is the source of the violence, the mayhem, the destruction. In every single one, every single area in the Middle East that is in flames, Iran is the source of those flames. The source, the inspiration, the ideological inspiration. Note that all these groups, with exception of the Syrian regime, all of them are Islamist, Jihadist, Sharia law, imposing, all of them are inspired by Iran, funded by Iran, armed by Iran, provided training by Iran, strategy of Iran. Now, the obvious conclusion for this should be that the only way to bring peace to the Middle East, the only way to bring peace to the Middle East, and I believe this has been true for 40 years, but it's only true over the last 20 since 9-11. It was, and it's certainly true today, the only way to bring peace to the Middle East is the absolute destruction of the Iranian regime. And nobody cares. Nobody cares. Everybody wants to evade that fact. Everybody wants to pretend that is not true. Everybody wants to delude themselves to thinking, oh no, we can deal with the Houthis separate from Iran. We can deal with the militias separate from Iran. We can deal with Hezbollah separate from Iran. We can deal with Hamas separate from Iran. You cannot, until Iran is liberated from the brutal theocracy that they have, this will continue. Or if it's impoverished enough, right, if it's destroyed economically, but that's the one thing no administration has been willing to touch. Yes, we had a sanctions on Iran, but there are lots of countries that violate sanctions and Iran was still bringing money more today than ever before, but did we destroy their oil facilities? That would completely eviscerate their capability of owning a living. No, we never touched it. Even as they, by the way, attacked a major refining operation in Saudi Arabia with drones, I can't remember how many years ago. They were flown by the Houthis, but basically by Iranian command. Even then, nobody attacked Iranian oil facilities.  Drones that are used by everybody, every bad guy in the world today has Iranian drones. Oh no, God forbid we do that. So the Bush administration evaded, if you remember, Lenin Pekov's four-page ad in the New York Times and Washington Post right after 9-11 declared Iran the enemy and that no solution was possible without taking out Iran. And that was true over and over and over again in the Bush administration, the Obama administration, in the Trump administration, and in now in the Biden administration again, Obama, Trump, Biden all tried to negotiate with Iran to no avail.  The immorality of our leadership, the immorality of our leadership that sticks its head in the sand, that pretend it's doing something is outrageous, truly outrageous and I think is indicative of how weak and pathetic and how cowardly American leadership is today. And the fact that American has no, no strategic vision, no foreign policy, no way in which to defend the individual rights, the lives of Americans going into the future. It's just America's just going to hand the world over to the Putin's, the Khamenei's and the Xis of the world. And God, it doesn't matter if it's a Republican or Democrat, as you can see with this immigration bill, they're all basically don't care. They're looking at the naval, they're gazing at the naval, they're gazing at the next election, they care about electoral politics, they care nothing, not zero for the well-being of this country and what is necessary for this country to thrive and succeed. Again, true of Republicans and Democrats, nothing. It's sad, pathetic, horrific.


What's up everybody, Jason here for JaspiesCaseBricks.com. 2022 Immaculate, three box R&B number four.  And of course we go distribute those hits if there is any. Via serial number break. You get a random number from zero to three nine. There's your examples there on how it works. Here's a dice roller, let's click dice roll. Four to one, five times. Here we go. One, two, three, four, and five. Five times, Ryan down to Stephen P. And we got five times here. One, two, three, four, five. Five, five, five, zero, down to nine. So Ryan you have zero, Mark with one, Andy with four, Ed with seven and three, Gregory with two, Stephen P with eight, Ryan with six, Gregory with five, and Stephen P with nine. All right, I appreciate you guys. Coming up next is the break itself. Good luck.


All right, so thanks to everybody who came to this last lecture. So let me remind you where we stopped last time, and I'll try to also get to what we'll try to do today. So we defined Ziegeltransform, so we had the function f from rd to c, and the Ziegeltransform took a function like this, and it moved it to a function on the modular space of lattices, so g mod gamma, the modular space of the unimodular lattices in rd, unimodular meaning that they have covolume 1, so lattices, I'll call the lattice delta. And so what were the Ziegeltransforms, so there are several different flavors, they're essentially equivalent, and if you can prove something about one, you can prove something about the other ones, but the relationship between them is going to be useful, and so it's good to have names for all of them, so the main one was the full transform, if you give it a lattice, it just sums the function at all the vectors in the lattice, including the zero vector, then we had the reduced one where we summed over the same collection of vectors except for the zero vector, so all lattices have the zero vector, so we can just forget about it, and finally we had the primitive version where we summed only over the primitive vectors, so remember primitive meant that no other multiple of the vector except maybe minus the vector, it was in the lattice, no other smaller, shorter vector proportional, but smaller vector was in the lattice. Okay, so there are two properties, so let's write like this, so the Ziegeltransform was any of these three, essentially it took functions, let's say compactly supported functions on RD, and it mapped them to continuous functions on g mod gamma, and if we took the reduced Ziegeltransform, it preserved up to some scalar multiple, so here we have Lebesgue measure to a one of g mod gamma with harm measure, so it was a bounded function in this sense, and the other important fact was that we had an action, so both on RD and on g mod gamma, we had an action on both of these spaces by g, which I remind you is SLDR, and this transform was equivariant, so we could act on a function here and then move it by the Ziegeltransform, and it would be the same as just moving it by the Ziegeltransform and then acting on this side, so this we had this equivariance property which was important, and we said that we can also consider the action on measures, so a measure is something dual to a continuous function, if you have a continuous function, and if you have a measure, it gives a number to every continuous function by integration, so since there are duals, the measures are going to go the other way, so if you have a measure here, you can produce a measure on RD, so action on measures, so if mu was, let's say, finite or, well, let me say just reasonable because finite is not enough, g mod gamma, then we define the new measure as a measure on RD by the following formula, we said that, so a measure has to take a function from RD and give you a number, so it takes a function and it first moves the function by the Ziegeltransform and then applies the measure on the other side, so again, this is, so we got this transpose maps from measures on, so reasonable measures on g mod gamma to reasonable measures on RD, and so the reason why I'm being vague about what's reasonable is because we're only going to be interested in a particular measure on the left side, so on the left side, you have a very natural measure given by Har measure, so what we have is, so we're interested in the Har measure on the side, where does it move over here, and so we said that, so we know it is SLDR invariant because it's a SLDR invariant on this side, so it will be, when you move it and this preserves the SLDR action, it will be SLDR invariant on the other side, so we would like to understand what is, what is it, and on the other side there are only two SLDR invariant measures, so it is going to be either, it should be some linear combination of the Dirac delta mass at zero and Lebesgue measure, so what we would like to understand is, first of all, what are these numbers, what are these coefficients, and yeah, so okay, so the first fact is that, so and you can ask the same question for any of these three transforms, you can ask where does each of these transforms take Har measure, and there should be some relatively simple relationships, so the reason why the full Ziegel transform is useful, so I mean, just notice what I said, so same question for the primitive, the reduced Ziegel transforms, where does, where do they take Lebesgue, Har measure on the left side, and so the first claim is that if you take the full Ziegel transform of the Har measure, then it's going to be the same linear combination of delta mass and Lebesgue measure, so in other words, if you use the full Ziegel transform, then you get everything, then you get the same number on both sides, so you have the symmetry, so why, why is this so, so the proof, so remember we had the Poisson summation formula, which went like this, let me write this here, so it said that if you take the sum, so this is true for any, again, let's say compactly supported function, if you sample it over all vectors of a lattice, it's the same as sampling the Fourier transform over the vectors of the dual lattice, and the Har measure on G mod gamma is invariant by this evolution, delta goes to the dual lattice, delta dual, and so this means that Har measure, for example, is preserved by this evolution, but on the Rd side, so if you look on Rd, Fourier transform, so Fourier transform of the Dirac delta mass is Lebesgue measure, and the other way around, if you take your Fourier transform of Lebesgue, you get the delta mass, so this means, so you get that whatever this, the Fourier transform of Har measure is, it is invariant by Fourier transform, and since you know it's some, some combination of these two guys, these two guys have to have the same coefficient, okay, so at least we know that there's just really one number that we care about, so the other claim, the other two claims which are easy to check, but will require a little bit more time, so I'm not going to do it, but at least morally it should be quite obvious, is that if you take the, let's say, the reduced Eagle transform, so really the reason you get this delta mass at zero is because when you define this Eagle transform, you're sampling over the zero vector, so if you don't sum over the zero vector, so if you take, if you transform the Har measure with respect to reduced, so without summing over the zero vectors, then you are just going to get, this is just going to be proportional to Lebesgue, and the same thing for the primitive vectors, in other words, there's no Dirac delta mass at zero, and the reason, the way you can see this is as follows, so what you can do is you can test on some functions, right? So the reason why we, so far we're just doing formal manipulations, but the reason why these concepts are useful is because you can actually test them on functions, and the function you can test it on is a bump function at the origin, very small, a small function continuous of integral one that's supported in the neighborhood of the origin, then if you look at this, for most lattices, this is going to be zero, because most lattices don't have short vectors, and so you get that this, whatever this transformed measure is, it does not have much, too much mass near the origin, and as you shrink the neighborhood of your support, of your bump function, you go, you see that it goes to zero, so you see that the transform measure gives no atom to the origin, so that's why you don't get any atom, you don't get any delta mass. Okay, so now we really have just one number that we would like to understand. We would like to understand this, well, we would like to understand, yeah, we'd like to understand this constant factor, and I'm going to first give you the claim, and then, let's see, yeah. So let me say the following. So, we're going to have a claim, and then from this claim, we'll see the, I don't know if I want to number these, maybe I'll say claim one, is that if you take the, which way do I want to, sorry, let me try to organize them the right way so that we don't have to prove the same thing many times. No, okay, so let me say the following, that forget about the claims. So, first let's look a little bit about the relationship between the primitive and the reduced Ziegels transforms. So if V is in the lattice, let's say non-zero, then there exists a unique, let's call it L and V prime, where L is in, is a natural number, and V prime is in the primitive vectors, such that L times V prime is equal to V. So this is just saying that if you have a vector, there's a unique rescaling of this vector that makes it primitive. So if, let's say, V is a one, a d, then L is the GCD of these numbers, and V prime is just a one over L, a d over L. Okay, so this is simple, this is just the definitions essentially, but we have the following exercise that you have the vector, let's call it V zero, one, zero, dot, dot, dot, zero, and then you have the group gamma SLDZ, and the claim is that for any primitive V prime, and V inside Z to the D, so for any vector, any primitive vector like this, there exists gamma and gamma such that gamma times V zero is equal to V. So it says that if you have a collection of numbers like this, which are relatively prime, there's a matrix in SLDZ with this as the first column. This is what it's saying, that you can always complete a vector like this with relatively prime entries to a D by D matrix such that the determinant is one. So this is your exercise. So this tells you that basically, so the last two things I wrote here tell you that the lattice is essentially composed of two things, of the primitive vectors and then successive rescaling of the primitive vectors. So this means that the lattice delta is the union, sorry let me call it delta minus zero, is the union over L natural number, L times the primitive vectors minus the zero vector. So it's the union of such rescaling. And so this tells you that the reduced and the primitive Z equal transforms, there's a direct relationship between them. So if you denote by M lambda, the operator of just multiplication by lambda, X goes to lambda X, then there's a way to connect these two guys. So the Z equal transform is just a summation where you apply the primitive Z equal transform, but then before applying the primitive Z equal transform, you rescaled the function so that you sample it on the larger vectors, a rescale of multiple of the vectors. Okay, so this is good. So now we want to understand how these things, so let's see how they act on measures. So if you take the transpose, so the this is going to be the sum of the T, right? If you take transposes, you should reverse the order. And so, so what do we get? So since if you apply the primitive transform, the harm measure, you get Lebesgue times some factor A times Lebesgue. And what does multiplication by lambda do to Lebesgue measure? What happens if you multiply by lambda and you apply that to Lebesgue measure? How does it affect it? So it multiplies it, but how much? If you multiply, if you have a transformation in the plane, you multiply everything by lambda. What does it do to Lebesgue? Sorry? So it's going to be lambda to the power minus d, right? So the question is, is it plus d or minus d? It's going to be minus d because take a circle of radius, a sphere of radius one, you multiply to make it larger and that has volume one. So this is smaller. So this is lambda to the minus d times Lebesgue. So this series now tells you that if you apply the reduced transform to a harm measure, then it's the same as applying the primitive transform and then scaling it. So this is just going to be one plus d to the minus, sorry, plus 2 to the minus d, plus 3 to the minus d, oops, plus and so on, plus the primitive applied to harm, which is Lebesgue measure. So we know that this is Lebesgue measure. So you get this, so you get that, you get exactly this factor which looks exactly like the zeta function. So you get that exactly as zeta of d times the primitive part, if you apply it to harm measure. So now we just have to compute the primitive transform of this harm measure and then we'll see what happens. So there are two claims. Let me make the following two claims. So if you take the primitive transform of harm measure, so this is claim one, then the claim is that you get the volume of a lower dimensional quotient times Lebesgue on RD. So the claim, yes, so the first claim is that if you just transform the primitive harm measure, you get a lower dimensional volume, which you might hope to know, and then times Lebesgue measure. So this factor is the slower dimensional volume and the second claim is that if you, so this is what I should have done in the very beginning. So if you take the, just the full, you take the full transform, so this is including the zero vector, you're going to get, so the factor that we wanted is the volume of G mod gamma delta zero plus Lebesgue on RD. And it's also the same as volume of G mod gamma times delta zero plus the transform, the reduced transform of harm. Okay, so let me try to discuss first claim two and then, before actually discussing them, let me show you that claim one plus two give the following recursive formula, SLDR mod SLDZ. It's data of D times the volume of the lower dimensional one. And so you get the promised formula that this is just going to be the product of the Zeta functions, the product of the Zeta values. Okay, so why is the claim one and claim two give you exactly this? It's because, well, we said that the primitive one gives you the previous guy and then the reduced one is the primitive times the Zeta value and the full transform is just the volume of G mod gamma times this. So you get that the volume of G mod gamma is equal to Zeta of D times this. So if you put these three, these formulas together, you get this recursion. Okay, so claim two is a little bit easier. So I'll just maybe say it in words. So there are two parts. This was from, so there are two equalities. So which one am I proving? So this, can you say it louder? I can't say it here. Yes, so one and two are, so these are independent of the normalization of hard measure. Yes, this one. No, but this is claim two, but there's claim one, which is dependent on the normalization of hard. So claim one, so I'm saying that claim two I should have done in the very beginning and I apologize. As you say, claim two does not depend on the normalization of this. If I scale this side by lambda, this scale also scales by the same thing. So claim two is true in general. Claim one is what gives you a normalization. So the content of claim two is just that first these two coefficients are the same. And the first coefficient is the volume of g mod gamma. So let me clarify claim two again is that the coefficient delta not in, if you just take the hard measure is the volume of g mod gamma, which is independent of any normalization. And the other part is that the coefficient of delta not is equal to the coefficient of Lebesgue or ST of hard. So it's just these two claims, which are scale invariant that they don't depend on the normalization. So this one, this equality was done using Poisson summation, which I did earlier. This part, so why is this, so well, yeah, so this is, let me call it A. Yeah, so A followed essentially because, so again, you take a small bump function zero. And if you compute it, you see that this function is essentially, because you're using the full summation over the full thing, you're going to get exactly the, that the function is going to be, so you test the, you'll see that it should converge to the volume of, you call this f epsilon, right? Then, then basically this is going, you should, sorry, and by bump f epsilon is one at zero and supported in epsilon neighborhood of zero. So then, if you take this f epsilon and you test it again, so you compute the Ziegler transform, so Ziegler f epsilon is equal to one at most lattices. So then the integral of s f epsilon with respect to R on g mod gamma is approximately the volume of g mod gamma. But at the same time, this should equal the volume of the transform, which is the delta mass, but this is the same as, you know, the f of, f of zero approximately should be approximately f of zero times the coefficient which we're interested in. Okay? And so this coefficient has to be this volume. Okay? Now, I've been completely honest with everybody, up to these approximate sides, which you can estimate here. Okay, so the upshot is that we just have to do this computation. So we have to transform the primitive hard measure. So what is it that we have to do this? So we need to compute, so for claim one, integral over g mod gamma of the integral of, sorry, of the summation of vectors and primitive vectors f of v. This is what we have to compute, right? We have to take a test function and integrate it on g mod gamma. So over all lattices, you, and then you start summing over these vectors. Okay? So remember, we had this structure. So we had something called gamma p, the stabilizer one zero zero in gamma, which is SLDZ and GP to be, again, the stabilizer of the same vector one zero zero in G, which is SLDR. So you see that these guys are just, so GP is just SLD minus one R, semi-direct R to the D minus one. So these are matrices of this type. So it's one stuff here and then D minus one by D minus one matrix. Can people see, should I write this, that left corner, that corner again or can, this I said earlier, this is by this Poisson summation. So the equality of coefficients is by this symmetry. Okay. So we have to, so let me know the thought. So in particular, this implies that the primitive vectors, so by the exercise I gave earlier, this is just, let me see on which side I want to do the quotient. Does it matter? Gamma mod gamma p, right? So they're identified with this kind of cosets because gamma acts on the lattice and the stabilizer of a primitive vector. So we're really summing over this coset. So now let's define, so let's observe that G mod of gamma p is equal to the moduli space of, so if I took the full G mod gamma, then I'm taking a lattice and I'm forgetting the basis. Here we're taking a lattice and we're not forgetting the basis, we're just forgetting the last d minus one vectors and the basis. So this is the moduli space of lattices, delta tilde, with a distinguished vector, primitive vector. So if you like it's delta tilde and v, so it's a lattice, delta tilde and then you have a distinguished primitive vector in that lattice. Okay. So you can see now that this moduli space is kind of, it's a nice moduli space, mod gamma p, it maps to rd minus zero by just a straightforward evaluation, which is if you have the sliders delta tilde v, you just map it to v and it also maps to the full moduli space G mod gamma. And so now you notice that the integral that we have over there, so we have this integral over G mod gamma of the summation of f of v where v belongs to the primitive vectors. This is nothing but the summation, it's just an integral over a bigger space. It's, you see the fibers over this point are just the choices of these possible primitive vectors. So instead of taking an integral and then a sum, we can just write it as an integral over this entire space. So it's an integral over G mod gamma p of just f of v d of delta tilde v. So this is, so we really want not just an integral and then a sum, we just have one single integral. So now, but notice that f came from here, f is coming from here, so this f is constant on the fibers of this map. So what are the fibers of the map? So the fibers of mod gamma p to r d minus 0 are just essentially cosets. So what's r d minus 0? This is g mod gp, right? So if gp is that s of d minus 1 r times r d minus 1 then this is, gp is the stabilizer of a point in r d minus 0. So it's again a homogeneous space under g. So you see we have g mod gamma p mapping to g mod gp. So the fibers are just together in the right side.  So you see now that this integral, so, and the other fact is that these measures that we're looking, higher measure here and higher measure here, and here you have Lebesgue measure, then they disintegrate in the right way. If you know, if with the correct normalizations they disintegrate in the right way. So you get that the integral over g mod gamma p of f of v is just the integral over r d minus 0 of f of v times the volume of this quotient gp mod gamma p.  So now about normalizations, the claim is that you can, if you normalize the measure in the right way on s l d mod r mod s l d z, you get normalize Lebesgue measure on r d minus 0 and then normalize Lebesgue measure on the next guy. So it's a computation, but they're induced natural measures on the next guy on s l d minus 1 r. If you start with one on the top, there's an, this vibration gives you induced measures.   And then these fibers, these are just story of constant volume. So they don't affect the integration. Okay, so we've proved the claim, we've proved the recursion formula with express the volume, the integral on this high-dimensional group by kind of lifting it to this guy and then pushing it down and showing that it's related to the previous volume, volume form. Okay, so we're done with Ziegels formula. So the conclusion is the following, that with the right normalizations, the volume of s l d r mod s l d z is just this product of zeta values. So now, since I don't have a lot of time, I'll just give two short applications which are quite nice and even if you don't care about these numbers, the applications are kind of interesting. So the first application is this. So the first application is suppose that you have k, a set, reasonable set, such that for any unimodular lattice, delta, k intersect delta is not empty. So suppose you have a set which intersects any lattice of co volume 1, then the claim is that the volume of k is also at least one. So this is kind of the converse of Minkowski's theorem which says that you have a convex set that intersects, you have a convex symmetric set and has sufficient large volume that it will intersect every lattice. This is kind of the converse. It says if you intersect every lattice, then you have to have some volume. And the proof is very simple. You just note the following. So take the Ziegler transform of the indicator function of k and this is at any lattice by assumption this is bigger than or equal to 1. And so the integral over g mod gamma of the indicator function of this transform is bigger than or equal to the volume of this g mod gamma. So here the normalization of the volume on this g mod gamma doesn't matter. But at the same time, since we know that if you take r, you get volume of g mod gamma times the bag, this was claim 2 which I wrote a little bit confusingly. But this claim was independent of the normalization of the volume on g mod gamma. It just says that take r by the full Ziegler transform, sorry, plus delta 0 I guess, but this is not so important. Then you find that the integral of 1k over rd minus 0 is bigger times the volume of g mod gamma bigger than or equal to the volume of g mod gamma. If you cancel it, you get the inequality on the volume of k. Okay. Are there questions? No. So let me, for the next application, I'll, we'll need just a very small strengthening of this. So again, k is, so now it doesn't have to be, it's not any set, it's a rate, like, so it's a symmetric respect to 0, respect to 0 set. And it is radio where, I guess, sorry, star shaped, meaning that if you have a point, it's, it contains all the points in between 0 and that point. So it's, star shape just means something. So that if you contain a lot, if you contain this point, you contain the entire line. So then, suppose that k intersects any primitive, any lattice except, it intersects it in primitive vectors. Then the claim is that the volume of k is bigger than or equal to zeta of n. So, sorry, it's even better, it's 2 zeta of n. So, I'll leave the proof as an exercise, but the point of the proof is exactly the same thing here, but now you apply the primitive Zegel transform. And you know that if a vector, if a symmetric, if I set like this, intersects the primitive vectors. It also, so if it intersects, if there's a vector v, then there's also a vector minus v, which gives you the factor of 2. And then the zeta of n factor comes from the Zegel transform factor that you got there. Okay, so you have this nice lower bound. So what can you do with such a lower bound? Well, one question which people about lattices have, people who study lattices have looked at for a long time is sphere packings. So how can you find lattices with, so we want to find a lattice with long shortest vector. What does this mean? It means that you, for any lattice, you try to, you look at what's the shortest vector in that lattice and you want that shortest vector to be as long as possible.  So in R2, you probably know that the hexagonal lattice like this is the best one. This is in R2. And then higher dimensions, not much is known. Okay, so the estimate which you can get, which is nice, is that, so using this method is the following. So let me just take the numbers. So there exists a lattice for this vector, bigger than or equal to what? 2 zeta of, so I apologize, I wrote D there, and there instead of D, or 1 over D. And here sigma D is the volume of the sphere of radius 1 centered at 0 in Rd. So you get this bound and this is, if you actually work it out, it's roughly a constant times square root of D. So it's not a, it's not a bad bound. It's definitely bigger than 1, or D large enough. And okay, so I don't want to go over time, so I'll just tell you what you do is you take, so set R as the minimum of all radii, or infimum if you like, of all radii such that the ball of radius R is centered at 0, intersects every lattice a non-zero vector. This is some number, it could be very small, right? This is the number we want, but it could be very small. But if you apply the bound that I just gave here, that the volume of this ball of radius R, since it intersects every lattice, it will particularly intersect in primitive vectors, the volume of that ball is going to be 2 times the zeta value, and the volume of the Rd, so the ball of radius R around 0 is just sigma D times R to the D. So you get exactly this bound on R. You get that R is at least this much. So you get, yes, I get this. I won't try it explicitly what these zeta values are, and what the volume is, but the explicit formula is, and this turns out to be roughly square root of D, which is not a bad bound. All right, so I'll stop here. Thanks for your attention of these four classes.


Hello and welcome to SCP Containment Breach with Dr. Sumerian. I am trying out a new format here, sound quality might be a little lower because the microphone is a little further away for me and it's also going to be mixed in with game audio so I'm not going to be able to clean it up as much as normal. I kind of am doing this as a bit of a test run. I want to see how it works for me and how it works for you, the audience. So this is a game I have a bit of a history with. We're going to go ahead and maybe we should make it Dr. Sumerian actually. Doctor, nope no dot. All right Dr. Sumerian and I've actually been playing this a little bit off and on. I actually had a failed recording a moment ago. The editing it I found out that the audio whilst basically running everything through the same recording at the same time so we'll see how it works out. Okay we're going to begin playing this game. I have a bit of a history with this. I played this in 2014 before I wrote my very first article for the wiki and probably without it I would, well when I first started writing in 2012 I wasn't exactly very good at it. Let's see am I D9341? Fair enough. In 2012 I mean you know how everyone starts off bad. You gotta practice in order to become any good and what ended up happening. By the way this is a very poorly designed bed. I get there are no supports on this side because it's coming out of the wall but there should be a support right here next to the wall anyway because otherwise you could sit down right on this corner and it would probably break. I'm just saying. Anyway back to the topic at hand before these guys show up and even if they do show up I'll keep talking. The thing is that when I first started writing it was particularly difficult for me because at the time the wiki was not exactly friendly to new writers so what I ended up doing was writing something that was terrible. Getting told it was terrible and then I was terrible for writing it and then I left and went and did other stuff for a while and then I started looking at Let's Plays like probably 2014 was when I first started basically watching Let's Plays and I saw Markiplier on YouTube and the containment breach playthroughs and all the others good stuff and hi. I need to turn that volume up a little bit. Hold on let's take a look see here. I don't want it to be so loud you can't understand what's going on but also the music is getting a bit too much. I like the music.   Nah it's not completely better let's give it a bit. I'll see one percent. No not there we go. We just got to get a little bit of that atmospheric background music but yeah without it I would never would have gotten back into the wiki. Attention please. I'm one of those few people they they call them the SCP containment breach kids. Please report head office. Hey. So you're seeing good movies lately? No I don't really watch movies. I read books. No what about video games? You know that reminds me somebody should make a video. Oh wait it's a really different story. The first time I heard that it was I don't really watch movies I read books. Can you hear Bolgan there in the background on the intercom? Well we're here still disappointed I didn't get to punch you in the face but yeah it happens oh and by the way let's take a look at the documentation for SCP 173 and I uh you know what hold on here I can't say but yet let's go in here and do the thing you know I remember playing this uh this has been updated a lot actually pretty good so hopefully you can still hear me uh over the trigger a thing so this is definitely gonna be a bad time for everybody. Crew 173 is down here because he killed me in the very beginning the very first time I played this well I'm not the very first actually he may have killed me the very first time I played it too but yeah he was definitely down here.


Hello and welcome to the session. Let us understand the following problem today. If a, b and c are real numbers and delta is equal to b plus c, c plus a, a plus b, c plus a, a plus b, b plus c, a plus b, b plus c and c plus a is equal to 0, shall add either a plus b plus c is equal to 0 or a is equal to b is equal to c. Now let us write the solution. We have delta is equal to b plus c, c plus a, a plus b, c plus a, a plus b, b plus c, a plus b, b plus c, c plus a equal to 0. Now applying r1 tends to r1 plus r2 plus r3.  Now taking common twice of a plus b plus c from the first row.  This we have got by taking common twice of a plus b plus c from r1. Now applying this is equal to 0. So now applying c2 tends to c2 minus c1 and c3 tends to c3 minus c1. We will apply the column operation on column c2 and column c3. So we will get now which implies twice of a plus b plus c, 1, 0, 0. First column will be written as it is c plus a, a plus b.  Now similarly b plus c minus a plus b is equal to c minus a. Now column operation for column 3, 1 minus 1, 0 which we have written here, b plus c minus c plus a will be equal to b minus a and similarly c plus a minus a plus b is equal to c minus b which is equal to 0. Now solving it further we get twice of a plus b plus c multiplied by 1 into b minus c into c minus b minus c minus a into b minus a which implies twice of a plus b plus c is equal multiplied by now we get bc minus b square minus c square plus bc minus bc minus ac minus ab plus a square which is equal to 0. Now we get twice of a plus b plus c multiplied by bc minus b square minus c square plus bc minus bc plus ac plus ab minus a square equal to 0. Here we see that this bc gets cancelled with this bc so we are left with twice of a plus b plus c multiplied by bc plus ac plus ab minus a square minus b square minus c square is equal to 0. Now which implies either a plus b plus c is equal to 0 or bc plus ac plus ab minus a square minus b square minus c square is equal to 0. Now first let us consider this it implies bc plus ac plus ab is equal to a square plus b square plus c square and this is possible only if a is equal to b is equal to c thus a plus b plus c is equal to 0 or a is equal to b is equal to c hence proved. I hope you understood the problem. Bye and have a nice day.


What's going on, everyone? Sam here with Leighton Sports Guard, dripping 23, Penny Illuminance, football hobby, um, six box break, number 26, random team style. Here's a look again at your random results. As always, you can find those on the website, under the results tab, as well as the link that's in chat. Good luck, everybody. Let's do it. More space. Nick Chubb on Leight the Beacons, the Browns, Zay Flowers, Ravens to 100, Kenneth Walker to 50, and Engaged, TJ Watt. Personally, I think it should just be in one, I think it should just be in Chicago every year. Chicago is like, I'd say the best venue for it. Why couldn't it be here? It could be here. I'm just thinking like Bijan, Jordan Addison to 175, Tai-Jay Spears to 100. That's true. And unforgettable Van Jefferson. My thing is, I think it should be in the Midwest, because it's the most central for everybody. You know what I mean? I think it should just stay in Chicago every year. I think Chicago is the most convenient traveling. Like it shouldn't be on any coast. Should not be in Atlantic City. It shouldn't be on the West Coast. Anthony Richardson. And I went to Atlantic City in 16, and I loved it. And I don't think it should be there though. Kirk Cousins to 150. Tyler Scott, nice one there, 350 for the Bears. And a Brock Purdy Vestige. Need to back in Baltimore. Now I know Baltimore was pretty popular. That was like 2000s and stuff. Bryce Young. Anthony Richardson to 200. One of 200. Jackson Smith and Jigba. Nice one there on the year one. Congrats on that. And Fugian, Justin Fields. Nice card to end it there. Should be in Detroit, yeah. How about that? Tai-Jay Spears. Nice one here. Reflected material, Eli Manning and Daniel Jones to 50 for the Giants. Tanner McKee to 50. Michael Parsons to 150. And unforgettable blue to 50. C.J. Stroud to 150. Chase Brown, rookie auto for the Bengals. Two, three, 50. Unforgettable, CD. Happy, oh god. Nolan Smith to 35. Good Lord, Joshua. The former trucker had to look. Will Anderson, auto to 125 Texans. And Amonra. Kansas City would be a good spot for it too. There's Michael Pittman to 150. Redemption, Darnell Washington, rookie luminance auto vertical going to the Steelers. Steelers, nice one there, Pittsburgh. Fugian, Bresaul. The only issue with having it here would be everybody's just going to complain it's too hot. Yeah. I feel like me being in Florida in summer. Yeah, yeah. You can still go to the beaches, you can go to the amusement parks, you can DJ more for the Bears. You can bring your family, not just, you know, come by yourself and trick them to say, yeah, that's what it is. Yeah. Nine of ten, K-Shop Beauty. That's who I do. It's at 150 Cooper Cup and Vestage, Jalen Waddle. Wake up in the day of the show, tight wipe. She leaves with the kids for the whole day. Run to the show. Hell yeah. There's Travis Etienne Jr. or Etienne Jr. 250. The Musgrave, year one auto, nice one for the Packers. Grats Green Bay. Vestage of Baker. I see videos of it all the time, Joshua. Roshan Johnson, Will Leviss Rookie. Quentin Johnson to 100. Josh Downs rookie auto for the Colts to at 25. Denver wouldn't be bad. Sauce Gardner. Yeah, it's got to be in a city that hosts a big show every year too, in my opinion. It's like Dallas could work, Denver could work, Atlanta theoretically could work. Atlanta's too crowded, dude. It shouldn't be in Atlanta. Tyra Wilson, nine of 35. It's way too difficult to get around in Atlanta. There's a redemption of Jonathan Mingo going to the Panthers. Nice one, Carolina. Carolina and Jay Jedis in Central Park, New York City. God. Mahomes. Nice one there on the Jumbo Jersey to 50 for the Chiefs. Drake London to 250. John Mingo to 50 and Kenneth Walker Vestige. O'Connell Tank Dell to 150. Cedric Wilson Jr. Nice one there. Go to 100 for the Dolphins. Nice one at Dolphins. Indianapolis would be good. Illuminated, Inc. If I want to talk about the best airport in the country, it's the Indianapolis Airport. Will Anderson. I love the Indianapolis Airport.  Kenny McIntosh to 175. Aiden O'Connell year one. Nice one for the Raiders. That's on that. And unforgettable DJ Moore. But the airport, it's clean. It's like cleanest airport I've ever been to. Super clean. A lot of food options. The seating is nice. I'm a big fan of the Indian Airport. There's Joe Burrow to 150. Zay Flowers. Rookie Otto to 10. Five of 10 for the Ravens. Nice one there, Baltimore. April Showers brings Zay Flowers, baby. Engaged CJ Mosley, like that one. April Showers brings Zay Flowers. April Showers brings Zay Flowers. What? I can hear you. Hello? Want to play kickball? No. I'll go and play that in elementary school. Reflected material is Javante Williams and Jamal Charles. On my day off? Yeah, would you come in on your day off and do that? No. To 50, Aaron Donald. Geno Smith to 250. Engaged Nick Bosa. I wouldn't even tune in on you. Did you just come in and ask me that? Tajay Spears. Israel Abacananda, or Abacanda. That's what it is. So, 350. There you go, Jets. And Savage of Camakers. What? Jay Caner to 175. Year one is Sean Clifford. He had a great pre-season actually for the Packers. Nice one there, Green Bay. Or Penn State, Nittany Lion. And Kenny Pickett. Go to a lot of Pacer games. Nice. There you go, Paul. I liked Indy. I really did. 250. Points ran to all at the end. It's an engaged Trayvon Walker. Will Leviss. Hadden Hooker-Rookie. And Deshaun Watson to 150. All right. Last box of the break. Good luck, everybody. There's Desmond Ritter. Great beginnings for the Falcons. Jersey Guard. Parker Washington to 100. Cleal Herbert to 100. And Savage to 100. Is Miles Sanders, the Eagle. Did you really just ask me that? You're going on a list. Hi, Travis Etn, Jr. to 35. Tana McKee, Rookie Auto for the Eagles. 15 of, or 16 of 50. Grats on that one. Eagles. And Nick Chubb, Vestige, Browns. Brace Young Rookie. Aidan Hutchinson to 150. Clayton Tune, nice one there. To 350 for the Cardinals. 182 of 350. And Fusion Mahomes. There's your card right there, Sean. Mahomes. That one's nice. And ending with another 250. Sorry about that, everybody. Ran to all. There's Josh Downes to 200. And Kenneth Walker Vestige. All right. Two, 250 points. I'll do the random here for you guys. Again, everybody is eligible for this. Again, going to roll the dice. Whatever two teams are on top, we'll get to the points after nine. Randoms, one, two, three, four, five, six, seven, eight, and nine. Ravens and then the Dolphins-Commanders combo. Congrats to those two teams. Paul, the airport in India is my favorite airport. We're just talking about that. The best airport in the country that I've ever been to. So we've got Desmond Ritter, reflected of Jamonte and Jamal Charles. Patch Mahomes. There's a DJ Moore. Daniel Jones Eli Manning. A Nick Chubb. Clayton Tune Otto. Tanner McKee. Sean Clifford. Zay Flowers to 10. Aidan O'Connell. Cedric Wilson. Jonathan Mingo. Luke Musgrave. Josh Downes. Will Anderson. Darnell Washington. Chase Brown. Jackson Smith and Jigba. Tyler Scott. And a Ty J Spears. I'm going to go for the break, everybody. Thanks again for the film. Coming up next is N.T.


The Minister of Defense, Major General Bashir Saleh al-Maghashi, has been advised to break the silence over what has happened to the $1 billion released by the federal government for the procurement of arms and ammunition under the past service chiefs, which were unaccounted for. The traditional ruler from Ayyedireh, local government of Oshun state Obadiqonli Makama, the law of Kuta, gave the advice while reacting to the current security threat to be deftly in the country. Obadiqonli Makama, who gave Kuta's terror to the Nigerian soldiers for defense in the country's territory, laying down their lives while battling the Boko Haram, urged all Nigerians to be security conscious and report all suspicious movements to security agents. The President know that the service chiefs are not the one that spend military arms fund. That's why he gave them what those who are supposed to say the truth did not talk. That's why sheklus starts lying and nobody stand up to them all. So is it not late? The minister can do good. If the minister rise up to their 10 Nigerians, because the document they don't online, they will sin. What the service chiefs use is their army budget, air force budget, Nama budget. You know, they have infrastructure budget. But this special intervention fund billions of dollars, Ministry of Defense, spend it on their air force. Ministry of Defense for the rise of spending through BPP. They procure equipment that will be received, so must they come. So that's it. But the country will forever be grateful to our former service chief, especially Abbasanoti Waiburaten, because he has created a namely environment for a visionary chief of army staff to follow. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.