Hello friends and welcome back to another episode here on the channel My name is Lee also known as Osiris and in today's episode We are gonna be doing something a little bit different from usual a little bit special We're gonna be covering and kind of reacting to a match that I took part in in the 2014 world championships in Washington DC It's a match between myself and Barys Akos It is round three of the world championships and for those of you that don't know I'm sure many of you do know Barys But he is the he's got a huge personality in larger than life German player like accolades coming out of his ears. He's got like amazing player He's got like national championships top eight at worlds regionals the list goes on and on and on So very well decorated player had an amazing career when he was playing And it was it was a real pleasure to play him at the world championships Very nervous at the time for myself Obviously I played Barys I think in the 2013 world championships the year before in Vancouver And it didn't go very well Barys kind of handed my butt to me that in that tournament But coming into this one it was a little bit different I had kind of I don't know I felt coming into the 2014 world championships Like I had something to kind of prove got my invite the year before For the 2013 in Vancouver and didn't really perform as well as I wanted to So I was very determined to kind of do well in this tournament And it turned out pretty well I ended up finishing top eight in this tournament finishing seventh overall And it's probably to this day my best finish in any tournament And probably my best kind of accolade that I've got personally And I just have a lot of fond memories from that year at world It was an amazing experience made a lot of friends as well that year And do look back on it very fondly And for that reason I kind of wanted to cover this match And it's weird that this match is available Because this was streamed by the Pokemon company It's a live stream going out But none of the VODs are actually available now And it's only because this French I believe they're French Poker blip Poker blip or Poker bip I don't know which one they are And they actually done I think it was a French commentary coverage of the event So this is the recording from from their side Their perspective Now the commentator is a commentator in my match We're Dwi and Justin Finn I don't think Justin doesn't commentate anymore Unfortunately he's a great guy And Dwi obviously does amazing commentator So we're going to look at this We're not going to have any commentary unfortunately But hopefully we can share this together and react to it Because like I say coming into this match I remember finish my round two this tournament And I remember just like kind of packing my stuff up And Barysh came across to me and grabbed me It's like come on we're on stream we're on stream And I was like oh no no I don't want to be on stream I don't want to be on stream especially against Barysh Because all I had in my head was like I knew this this more while And got the telco was going around the tournament Like people were talking about it I was like I know Barysh is playing that I don't know really what it's do And I don't know the team archetype is very new No one had really been playing it prior to Worlds At least that I knew of And I hadn't played it at all I hadn't practiced against it So I was worried about that And I was also like the last year I played them It didn't go so well So had all these thoughts gone through my head So I wasn't feeling the best about going into this match But we got up onto the stage You'll see this in a minute as we'll start off From the beginning you can see there's the stage there And then coming into the team preview here So just a little bit of backstory about 2014 as well 2014 was the year that Mega Pokemon were introduced to the format in X and Y Which is an amazing thing Obviously Mega Kangaskorn was the big mega It kind of dominated the entire season Winning regionals, nationals Like everything it won So coming into Worlds It was definitely a Pokemon that had a big target on its back And everyone was kind of gunning for it And you kind of were expecting a lot of Mega Kangaskorn But it turned out there wasn't really that many Mega Kangaskorn And I don't think any cut There might have been one that cut I'm not 100% sure though I don't think any cut But a lot of Mega Mobile To kind of counteract the Kangaskorn As you can see Barus's team here Is a polytore of the Kingdra Which is a really nice rain call Rain very strong that year as well Not so much with the Kingdra You normally saw Ludicolo So the Kingdra was a nice pick Obviously faster than Ludicolo as well So it gives you like a little bit more offensive option there But without the fake out And then you've got Moel, the Kangaskorn Both Mega's So a double Mega team Really nice flexibility as well With the trap from the Gothatel And then rounding off with Zapdos So a really nice team And pretty scary to kind of face off against in team preview Now my team I had three of the same Pokemon as Barus I had the polytode The Moel and the Zapdos But instead of Kingdra I had Ludicolo Instead of Kangaskorn I had Garchomp And then instead of Gothatel I was playing Taranitor So I was playing a sand and rain kind of call This year And I figured like double weather Give me the most flexibility Most options to play around I definitely wanted to play Mega Moel As my Mega It was something I played at the very start of the format And I kind of fell in love with From the very beginning of X and Y So it was something I wanted to go with And I love polytode Ludicolo was one of my favourite calls From early generations And even into X and Y So as you can see We're going into it There's the players down in the bottom corner There's Barush on the right And then myself on the left there As you can see Big zoom up of me I don't know if I look much different Probably look a lot different than Barush there They're looking all like he does Glowing, glowing But yeah I was seriously nervous about this match I was like I really didn't I wanted to do well And I thought Round three I don't want to lose That's the big thing And I knew the goth hotel was a big threat In Team Preview So I had to My only thing that I could lead Here to kind of get around The goth hotel Give me a pivot out Was my Zapdos It was fast and it had Volt Switch So I knew that would give me An option to kind of reposition I couldn't exactly gochomp here Because the Intimidate really does Kind of slow the momentum down With gochomp from the opposing Moel And I thought if I get in a trick room situation I'm trapped with gochomp on the field Against a Moel in trick room It's like it's going to be game over Especially Intimidate So my idea was really to Try and pivot out with Zapdos Get gochomp in And just use my Moel Intimidate To kind of slow Barush's Moel If it came in And anyway Leading the Zapdos Give me a decent-ish kind of matchup Against the Raincore as well As we'll see in a little bit But this is the first match We're going to see both Moel's Mega Evolve And I think mine Mega'd before his So indicating that his is the slower one So if the trick room does go up Like we're suspecting here Then it will get a little bit tricky for us So we do go for the Vault Switch Suspecting that you know The Gothetel's going to trick room So that's the slot that we can definitely pivot out on And this gives me the opportunity To get gochomp on at the field Which is amazing And the thing is you would think Okay well Gochomp's not in the greatest position here We are in a trick room Against a Mega Moel But I built this gochomp Specifically for the World Championships Thinking that Moel could be quite a popular Pokemon And it was actually built to take Mega Moel on Like one on one and always win Because we're holding a Rose Ellie Berry And gochomp's EV to take a play rough And then a Sucker Punch from a Moel Unintimidated as well So we've got the Intimidated onto His Mega Moel right now So I felt really comfortable in this position I know the Moel's just protected as well So I've got a pretty free Earthquake This turn As we see a fire fang from his Moel into mine We do protect and the psychic doubling in On our Moel But we do get that Earthquake here And we do get some nice big fat damage Onto both Pokemon And put both the Gotha Tel And the Moel into very close KO range So one more Earthquake will do the job But I can't really Earthquake this turn Because of my Moel out on the field And it's kind of a bit counter productive If I do go for an Earthquake here Just because we'll just be damaging our own Moel Which won't help But we do see the fire fang It's a nice tech as well It wasn't really something you saw very often on Moel's But for the Moel Mira It's a very good option We go for that Iron Head It's in low enough range to pick the knockup out there Obviously being part fairy as well It's not resistant It's just neutral And then a Dragonclaw Cleans up the Gotha Tel Removes the trap And we're sitting right now In a very good position But I don't really know if you can see I'm very very kind of like I'm not very reactionary Like I don't react very much in matches at all Like you never would see me pop off Or anything like that Very rarely anyway And I like to just try and concentrate Until that very last turn Why I definitely know I won Because otherwise I feel like in big high situations like this I get very complacent Like I don't want to get complacent And I feel like if I get ahead of myself That's what will happen And I can let my opponent back in So if I stay very very concentrated In my head Then it works at least for me So we've got the Zapdos And the Polytod coming in Now we're still in Trick Room So we're not in the best position at all Gotchomp Not in any good position Against an Ice Beam Potentially Polytod And Hidden Part Ice From the Zapdos So we do protect here We see the Ice Beam From the Polytod We do underspeed the Zapdos Which is nice And manage to get a play rough off And do some good damages The Zapdos does take more while down But I think here I'm thinking that I've probably got Tyrannotor in the back So I can bring T-Tor in now Which gets rid of the rain It gives us a little bit of a better option Against the Polytod And definitely a better option Against the Zapdos Yeah it is the Tyrannotor And it's strange Because I wasn't running a protect On my Tyrannotor I wanted Thunder Wave And I wanted Taunt Which seemed like the craziest Options ever To run on a Tyrannotor And I think I had Assurance in Crunch Sorry Assurance in Rock Slide Was the Mild Move Set With the Lumbary And the Taunt was there To really help me shut down Opposing a Moongus I didn't want to get like Spored And was it a Moongus Or was it I don't know if a Moongus was Oh a Moongus was in this I'm pretty sure There's a Moongus in Smiggles as well So I could always get the I'd always wake up And then be able to taunt Opposing Smiggles And obviously taunt A Moongus before they could do Anything like that But we get the Rock Slide off Take the Zapdos down Obviously we're slower Than the Zapdos as well And then we switched out Garchom Keeping for later The dimensions turn back As we get a Zapdos onto the field And now we can just Thunderbolt And take the Polytod down Pretty easily And that's like a nice Easy game won for us I feel like we do have a good match-up Against the Barrages team as well So we get the little cheeky handshake there But yeah Like I felt good about that It was nice to get the win Obviously to take that first game But it's like it's still not anything Like I always feel like If sometimes if a game goes that well Early on You know the second game Is going to be like that much harder Because your opponent at this high level As well they're going to be Throwing everything at you To claw the game back And if you lose that second game I feel like it's almost even more difficult To win the third game Where your opponent's got all the momentum Going into that third game Coming off a win in the second one If that makes sense anyway So it's like even higher stakes Going into the second game for me Just to try and lock it up Because if you can just nick it here I still have a lot of tricks on my team That I haven't revealed in game one Which is very nice Like we haven't revealed the Roselli Berry We haven't revealed the item on Tyranitar And I don't think we've revealed the item on Zapdos either Which is a big key imponent Because we're running Scarf Zapdos as well And I don't think I'm making that many waves At the tournament yet Just round three that I have Need to be worried about people Scouting my team or none Like what items and things I'm running So I'm probably at that stage of the tournament Where I'm kind of just mowsying along And no one's really noticing So that's quite like a benefit for me So we actually see him changing up here With the Kingdra and the Polytod Which makes things a little bit more awkward for us Especially for... We really need to just get rid of the Kingdra If we can get rid of the Kingdra Things become a lot easier for us The Polytod I'm not too worried about Because I think we've got Tyranitar I think we've got Tyranitar and Garchomp in the back I think we've got the same two in the back But I just need to get rid of this Kingdra This is the big problem for us They need to get rid of the Kingdra Once that's gone Like we've got the fastest thing on the field then Because with my Zapdos It's scarfed, it outspeeds Max speed, modest, ludicolor in the rain So we always get the jump on that But that doesn't give me the jump on Kingdra So in this matchup This is where it was very awkward for me Because I was like Okay most of the time I can kind of catch my opponent off guard They're going to let their guard down with the Polytod Potentially because the ludic can hit us first But in this situation I can't actually Outspeed the Kingdra Which is a little bit awkward Now we do see it go for a muddy water And it does big big fat damage So I don't know whether that's specs or not I would expect it to be choice specs No it's life orb, sorry Life orb Man life orb does so much damage Does so much damage You get the play rough off and manage to survive We've got quite a bulky Moel And the Kingdra is down there So I think if we hadn't had as much bulk in our Moel And we wouldn't have been in such a good position Because that probably would take down no Your normal 252 HP Moel pretty easily there The thunder obviously going into the protect there Of the Polytod And the interesting story here I'm going to stop here Because this zaptos Right, we've taken quite a hefty amount of damage With our zaptos Now this zaptos Right I wanted for this tournament I wanted if you look at the team We've not got very much coverage against grass types And I was worried about Venusaur in particular And I was like I need an answer against mega Venusaur I know Moel doesn't do a bad job But I can't just rely on that 100% of the time Because they're going to have probably fire types To kind of cover the Venusaur and things like that So I was like okay Where can I fit something on my team To kind of help with the grass matchup The Venusaur matchup And I was like well Titor We could play Icebeam But then it disrupts the move set that I've got already And I'm really kind of set on the move set Rock slide assurance T wave and taunt I didn't really want to change that And I was looking around the other team There isn't really many options Ludicolor Polytod isn't really a matchup You want to bring against mega Venusaur So I was like The only option is zaptos And hidden power flying So I was like okay I remember booting up my Y copy And I'd already caught zaptos in my X So I was like okay I need to try and reset for hidden power flying Zaptos And I'm not even exaggerating here It was like literally three weeks of soft resetting For the zaptos And I had no luck I had no luck getting it Literally on and off Like I used to commute like three hours a day to work And I like was soft resetting on the way there We're home And like I had no I literally didn't get it Flew out to Vancouver And it was the night before we had to lock our battle boxes For the tournament And I still hadn't got it And I was like panicking at this point I was like I'm literally not going to get it for the tournament I need it for the tournament And I need this This hidden power flying zaptos It was a weird spread I think it's like 31, 31, 31, 30, 30, 30 So you needed all odds and then all evens I'm pretty sure that's what the mix was there So it was an incredibly difficult spread to get And it came to like an hour before I went to bed That night And I soft reset And I managed to get it But it turned out the zaptos had like zero special defense IV It had really bad speed This is before you could hyper train or anything like that as well So it was like it was really like it was terrible So I had to like rearrange the whole EV spread And I was just like Okay, well I'm going to have to sacrifice any sort of bulk I've got on the zaptos Which was a good amount of bulk And then just max out the speed to get the speeds that I need Because that's the most important thing And then just put the rest in physical attack Because sorry, special attack And just like forget about any bulk And just have to go into the tournament like that Because I've got no other option I can't afford to soft reset now After just getting it after like three weeks of soft resetting for it So it was like it was a night It was a bit of a nightmare But it worked out all right in the end But this zaptos Taking a lot more damage there from the muddy water So a little bit of a back story More well coming in now getting the Intimidate Which is really big on to our more well And we've obviously now got to worry about sucker punch But at this point I'm like does he have sucker punch Because he's got the fire fang Normally you have iron head, player off, sucker punch Has he dropped sucker punch and just got fire fang So it might mean that I can get a thunder off into this polytod So I can't really remember what I go for In my head I would be like Let's go for the thunder into the polytod Let's try and get rid of it And get some damage onto the field Because if zaptos goes down now then it's fine We've still got plenty of pokemon in the back to come in And it would mean that Garchomp could come in As long as we get some damage onto the opposing polytod now Without more while But no, we're not, we're switching out Okay, okay, okay We switch out for Tyranitar Okay, well that makes a bit of sense I guess just to get rid of the rain Does more while just protect here? Okay, polytod switching out And getting the gothatelle on the field Okay, I wonder if I was reading this at the time I feel like, I don't know I don't want to blow my own trumpet But I feel like this is maybe something that I was scared of If the gothatelle comes out onto the field And then I cannot switch around And he gets a trick room up in a more well In an amazing spot So we protect We see the more well go for rock slide Okay And it's not intimidated now Which is a little bit tricky Now this is where the Tyranitar comes into play Okay, so he's got the gothatelle out on the field He's going to go for the trick room Never suspect in a million years That we've got taunt on our Tyranitar And this is one of these specific moments Why I chose to run taunt And I think, you know, looking back at the tournament I think I did make some good picks With move selections on my Pokemon for sure I think they definitely came it They were really pivotal And how well my performance went that year So I can't really complain too much about it We get the taunt into the gothatelle Get a nice iron head into the more well And we take a play rough Which takes down Tito But it's done its job Okay, it's stopped the trick room going up And this means now that we can get Garchomp onto the field Which is amazing because we stopped the trick room And then, yeah, like I say Garchomp can come out onto the field now The more well is in knockout range So we can just I think switch out more well Of our own into Zapdos is a pretty safe switch Because then it allows us to go for the earthquake Pretty freely and keep more well Maybe for a little bit later on And then if the poly toad comes onto the field as well It does mean that Zapdos can put a lot more pressure onto it Rather than just having more well It's probably going to be slower than the poly toad And get knocked out from the range that we are right now So I think that's what we do next I'm pretty sure I should have watched this back first But I feel like it's better experience Like watching it together live Well kind of live, not live But you know because I it's been such a long time Since I've seen this match And oh my god Wait there, wait there Oh my god, look Okay, so have you read the title here Leap provost versus Boris Oh my god Boris Boris I cause How can they get this wrong? How can they get this wrong? It's barish Like on the screen How can How can they get that wrong? Sorry, sorry, sorry Okay, well we'll get back to to Lee versus Boris I don't even know if barish knows this is up I've got to point this out to him I'm going to have to send this to him Like that's never ever anything that I would have ever made a mistake for Okay, so we don't switch the more well out for Zapdos We just protect it and we go for that earthquake We are seeing the more well switch out though And the polytod come back in So it's quite important that we get decent damage onto the polytod We get very lucky there and get a critical hit Which like we do way more damage than we should have done To the polytod there which makes things a lot easier for us going forward See psychic into the garchomp And now we've got to be worried Because our special defense falls And obviously the polytod we've already seen has got ice beam This goth hotel isn't going to be taunted for that much longer So it's got like a maybe one or two turns where it's taunted So we need to make sure that we're getting damage onto it Like now really So we see protect from garchomp Might have to feel want to preserve that And we get the play rough into the polytod Okay, so we must have known That we were faster than the polytod Which is a big deal for us We see the skull come out into our more well Pick up the knockout But this is fine now Because this means that we just get zaptos onto the field And we've got the discquake combination Which is one of the main reasons why I wanted to play zaptos garchomp this year So running discharge on zaptos Garchomp immune to it with its ground typing And then we can earthquake as well It's a really old school combination But very effective as well So we can just literally earthquake and discharge And clear the field now And then more well can come in We know it hasn't got suck a punch And that pretty much wraps up the game from us From this point right now And I'm kind of feeling like Okay, nothing going seriously wrong Like misclicking or anything like that We should have wrapped up this one And that would take us to 3-0 With two more rounds Is it two more rounds? Two more rounds? No, 3-0 with three more rounds left To play in the qualifier rounds So this is equivalent to like day three What you get now But we didn't have like day We didn't have a day one It was just the lcq and then the main event So the goth hotel going for the protector And we'll go for a nice juicy discharge Which gets rid of the polytod And being scoffed at us as well Really helps us out And then the mobile just to come in As the taunt is worn off on the goth hotel Obviously I was a little bit worried I think at that point That the goth hotel may survive Like this combination Because the goth hotel can be bulky And if it survives then that would mean It would lose the game I'd lose the game If the goth hotel got to trick him up That would be it There's no coming back from this point So we've got ourselves into a good end position here Where like we should be doing enough With discharge and earthquake To kind of clean this game up So we do see More while going for that protect And that's the right player Because like I say If goth hotel can take this combination Which Depending on how it's built You know Depending on what happens So he takes the discharge pretty well We do get the paralysis He can see me there Just apologizing for the paralysis But I don't really think it comes into play Doesn't matter Because I think the earthquake Is more than enough to take down the goth hotel And then there's just a more while there But we do manage to wrap this one up Pretty easily I don't know if we see a forfeit I don't even Yeah, I think we just I don't know if we forfeit in these ones Because we are on stream So we'll probably finish it out As you're advised to On stream If you're on stream Finish your matches Don't forfeit Ever And that's Aptos Was on fire that tournament as well We get the Like discharge paralysis Is nuts as well So it's very handy But the speed tiers are Like the speed mechanics Are very different back here Than they are on Sword and Shield But we do wrap it up And honestly to this day now It's like it's still a match That I look back on very fondly And like I say It was a massive pleasure to play Barish And he's an incredible player So getting the result there Was like really nice And I think even after the match I was like I was still like a bit like You know Just don't know what's really going on Just focused on the tournament On my next match And just trying to do well And I think I play I'm not sure who I'm playing the next round Can't remember Might have been Colin Colin Hire Might have been No I think I play Colin Yeah I play Colin round 5 I play Colin round 5 I can't remember who I play around 4 And then I play Marcus Liu in round 6 I believe And then I finish I finish Swiss 5-1 I think 3rd seed Or something like that I can't really remember I think it was 3rd 3rd seed And then go on to play Judy And the The top 8 in the quarterfinals And Judy wins And then goes on to the final to play Sazion And that like Iconic final with Patrice and Sazion Kind of taking the championship that year But there we go That is it my friends It's that's been a really fun video I've really enjoyed it So there's many more matches out there That we could look at And do this sort of thing on But I thought this was quite a nice one To come in with Just talk about a little backstory of myself As well as some of my experiences And look back at an old match as well That I have like such fond memories of And just share that with you guys So I hope you've enjoyed it It's been a lot of fun doing it If you'd like to see more of these episodes And things like that in the future Let me know But leave your comments down below Let me know what your thoughts are on the match And if you ever did watch that live Or if you were involved in that season Or anything like that I'd love to hear your experiences from that year At the World Championships It would be a lot of fun to hear about those as well Or just that season as well Obviously the 2014 season was incredibly amazing We had a huge Pokemon boom that year With X and Y And it was a lot of fun And hopefully Even though we've got the current situation Going on at the minute in the world Hopefully we can get back to live events In very near future And kind of have these experiences again Because they're a lot of fun And meeting and making new friends And stuff like that But that is for another time So I'm going to end it there friends Hope you've enjoyed today's episode Really thanks for tuning in And I look forward to reading the comments And see you all for the next one So until then friends Take care of yourselves and bye bye


Hello everybody, Hood and Copper Commander 788 here, and this is a very quick look at the 1984 VAMP Mark II, and the VAMP Mark II was almost an entire reuse of the original VAMP mold from the 1982 vehicle. The 1982 vehicle of course was green, and this is more of a tannish brown, more of a desert camouflaged color scheme. They did add some details, they added the shovel here to the front end, looks like they have some kind of a bag here, different gas cans on the back, and probably most importantly, instead of having a gun on the back, which the original VAMP did, this has a four-missile missile box. They didn't just add detail to it though, they also added some coverings for the cab, some doors that swing open connected to this bar here, and a canopy at the top. The passenger side door on mine is broken though, here at the hinge where it connects to the bar, so I'm not sure if I'm going to consider this ready to review yet, since we do have one broken part, but maybe we might just consider that good enough. The VAMP Mark II came with a driver, as the original VAMP did, it came with clutch, but this second version of clutch, instead of having a green uniform, had a light tan uniform. When I do a full review of it, of course I will compare the VAMP Mark II to the original VAMP, but this is just a quick look at it for now. I hope you enjoyed this quick review, and keep an eye out on this channel for more full GI Joe Tour reviews coming up. Thanks for watching, and I'll see you soon.


I was pretty bad in the first couple but got it together, got my bike working a lot better for the last three races or whatever. Maxi did excellent. Jayman did his job when he came in and we managed to get enough points together to get through so we're pretty stoked with that. Really disappointed, compared last year we couldn't repeat that performance here and my own own meeting went unfortunately a little bit downhill. Only two races, I messed the third one up but I'm pleased with the performance and the whole team pulled together and done good and we got the win. Started off really good for myself and then we were sharing setups and working well together I think. Just chipping away and getting good points all the way through the meeting so for Team Australia it's really good. It's great to be going straight through to Russia now. Obviously got good points but I feel like we're just lacking a little bit but it's something to work on. It's still early doors for me, I've only done a handful of matches so we're still working on it. We're still looking for a little bit extra but yeah good start to the meeting and obviously good meeting overall. Great that we've finished top. Definitely rode hard and nobody was slacking, we were all giving our best and we're fighting so that's a good part. At least we made a good impact and missed it by that much but like I said before that's racing and it's all part of it. We probably had potential to win the meeting today but we did it the hard way by going through the knockout race. Obviously we're disappointed because when you're that close you want to go through but yeah that's the way it is. As I said we've been a bit unlucky but we give our best all night and that's all we can say so that's about it.  I won three British championships, been so close to doing it at Cardiff. So many British fans have been over to Torrent to watch me lift the world championship and when we can give them back a little bit of something like this tonight then it's just spot on. So I'm sure they've all had a good night and yeah thanks for all coming and cheer on Azon. It's always a pleasure to be back here.


In this video, I wanna show two more examples of how a typical induction proof looks like. When it comes to an induction proof, there's always three parts. You have a base case where you're gonna prove that the statement is true for basically the smallest natural number that's appropriate. Then you're gonna do the inductive hypothesis, which is just a statement of an assumption. You're gonna assume it's true for an arbitrary case. And then you'll have the inductive application for which then you'll prove that the next number also has the property because of the inductive hypothesis. And those three ingredients together give us a typical induction proof. So with this one right here, let's do a divisibility type argument. Maybe you'd do something like this in number theory. Prove that every integer of the form 10 to the n plus one power plus three times 10 to the nth power plus five is always divisible at nine for any natural number n. And so the proof right here, it's usually good when you start a proof by induction to say that what you're gonna do, right? So we'll say something like we proceed by induction. Now, when you're watching these videos, I wanna make you aware that when I write these proofs in real time, this isn't the best polished proof. You might wanna go to the lecture notes, which are linked to this video to actually see a better looking version of the proof. The reason I'm doing this in real time, as opposed to just reading a proof here, is that this is meant to be instructional. As a professor, I'm trying to teach you how to write proofs, right? And so I wanna write it in real time. So you know what I think about when I would write in a proof here? Different styles, different structures of the proof. Although this is not necessarily a final draft of a proof, I'm trying to show you the structure of how one does these type of proofs. So you should start off by telling people what you're gonna do, right? We're gonna proceed by induction. You don't wanna just kind of randomly walk through a proof and leave the audience unaware of what's going on here. It's like, what you should tell them we proceed by induction or something equivalent to that. And if you wanna actually enumerate the parts, you can do that. I don't necessarily do that myself when I write the proof, but as your professor here, I'm gonna indicate exactly what we're doing here. So the base case. So we wanna consider what's the smallest natural number for which this property is gonna be true. And although n equals one makes sense, it turns out we can be a little bit better, n equals zero. When you're improving stuff by induction, it's always a good idea to think about what n equals zero makes sense. And if it does make sense, I would actually include that as the base case. So let n equals zero. And so then consider in that situation, your number, right? You have 10 to the n plus one plus three times 10 to the n plus five. That would look like 10 to the first plus three times 10 to the zero plus five. 10 to the first will of course be 10. 10 to the zero is a one.  This adds up to be 18. 18 is two times nine. And so therefore it holds for the base case. All right, so that's kind of like our base case. So we finished it, so now we move on. Great. So then we go to our inductive hypothesis in which case we're going to assume assume that nine divides the number 10 to the k plus one plus three times 10 to the k plus five for sum number k, which is great equal to zero, right? That's one way you could phrase it or another way you could say it like, so there exists some integer, what do I wanna call it? Let's call it say m. There exists some integer m such that 10 to the k plus one plus three times 10 to the n, 10 to the k, excuse me, be consistent in your variable there plus five equals nine m. That's what we'll do. So we'll actually have the multiple specific here. Now to the inductive case, right? So now using the inductive hypothesis we wanna consider when we take n to be k plus one. So now consider the case when n equals k plus one. So we're gonna take this number. We're gonna take 10 to the k plus two plus three times 10 to the k plus one plus five. We wanna show that nine divides this number in some way or another, okay? And so this is why proofwriting is a creative process because the next step might not be obvious why we take it as one explores these problems and just kind of see natural to do it here. It's like, okay, what's the next step? Well, I have to somehow find the number 10 k plus one plus three times k and plus a five, right? And I kind of have that here, but I have an extra 10. Maybe we should factor out that 10. So for example, if you factor out the 10 from the first two numbers there, you're gonna get 10 times 10 k plus one plus three times 10 to the k, like so. And then you have the plus five still. So it's kind of what you have there. It's like, well, you know, I almost have what I need except I need a plus five right here. So what if I just add a plus five, you know? No one's looking, you sneak it in there. Well, we want it to be true, right? We need equality here. And so if we add a five, we should just subtract a five. But we really didn't add five. We took 10 times five, right? So this 10 would distribute onto each of these terms right here, right? So this is kind of like when we complete the square. So we're gonna actually subtract five times 10 to balance out the five we added there. The reason why this is useful is that this number right here is then by our inductive hypothesis gonna equal nine M. And so this is how we're using the inductive hypothesis when we use it right here. So continuing on there, we're gonna get 10 times nine M plus five minus 50. Like so, simplifying this, we get nine times 10 M minus 45. Oh, looky there, 45 is a multiple of nine, isn't it? It is nine times five. So we get nine times five. If you factor out the nine, you're gonna get nine times 10 M minus five. And therefore we see that nine divides the number in question here. And so this is exactly what we were trying to show. And so that then proves the inductive case. And so then we conclude with something like therefore the result follows by induction. And that is how our induction proof will work. We had our base case, our induction hypothesis and our inductive case. That's how it finishes. Let's look at one more example of this. This time, we're actually gonna prove it in equality using induction. Again, this is gonna be a little bit more tricky than in an equation, but the principles of induction are gonna work the same way here. As we try to prove it, this is gonna be approved by induction. So we proceed by induction. And so we're gonna first consider the situation. What's the right natural number to start here? Oftentimes they should tell you, I'm gonna start with n equals zero because n equals zero, the statement's true. So notice when n equals zero here, you're gonna get that two to the zero is equal to one, which is greater than zero, like so, great. And so this, whoops, this proves the base case. So we have some base case. I usually like to start with the base case. So then next, we'll make our induction hypothesis. Assume that two to the k is greater than just k for some k greater than or equal to zero. This is our inductive hypothesis. Now, consider the case where n equals k plus one. So you're gonna have some inequalities here, right? You're gonna have two to the k plus one. We have to somehow relate this to our inductive hypothesis. So I'm gonna probably do that by factoring, two to the k plus one is two times two to the k, which then by our inductive hypothesis, we know that two to the k is greater than k. So this will be two times k right here. And again, it's a good idea to be explicit here. Our inductive hypothesis was used on this inequality right here. And so now, well, how do we connect this to what we're looking for? Two k right here, well, two k, this is equal to k plus k, like so. And k is actually gonna be greater than or equal to one, k plus one here. And so we actually, since we already took care of the base case, we could actually, which is zero, we can actually say that k is strictly greater than zero, right? I guess actually, I have to be a little bit careful here. We want k plus k to be great equal to one. So the thing is, this is where it gets a little bit fishy, right? It turns out that the argument doesn't quite work when k equals zero. We actually need that this thing is greater than or equal to one to make the following argument work. So that if k is great equal to one, then this k is great equal to one. And then we get the statement we want right there. And so in this situation, you might actually be justified in doing a second base case. Sometimes you need to do that. Let's do n equals zero or n equals one. If you take n equals one, that's equal to two, which is greater than one, it's not a big deal. If you have to do an extra base case or two, that's perfectly fine. Do as many as necessary so we get this thing to work, right? It's true for zero, but for this argument to follow, it kind of needs to be greater than equal to one. So we make that statement right there and then we're done. Therefore, the result follows my induction. And so this gives us two more examples of a typical induction argument. And in the homework, you'll have plenty of opportunity to practice this principle some more.


Hi, everyone. Welcome to today's webinar, where we'll be talking about how to stand out as a B2B product manager. Let's get started. A little something about me. My name is Richa Bala. Currently, I'm based in Amsterdam, where I work for Booking.com, one of the world's largest online travel agencies. A lot of you might not know this, but Booking.com is actually a two-way marketplace, meaning that there is, of course, a really strong consumer side of the business which travelers like you and me can use to book our hotel stays and our flights. But there's also a very prominent partner side of the business, or a B2B side of the business, which is where I work. I work on a reservation side, which means that whenever you go and book your stay through Booking.com, my job is to ensure that that reservation information gets communicated to the property you're staying at immediately. So they're aware of your upcoming visit and they can prepare for your visit accordingly. Before moving to Booking.com, I was based in a city in India called Hyderabad where I used to work for a B2B SaaS company called Gainsight. Gainsight is a customer success platform and I managed their customer experience suite of products. Before Gainsight, I also spent a couple of years at Standard & Poor's S&P Global, which is best known as one of the top three big three credit rating agencies. I worked at S&P for their credit analysis business as a product manager and also in their cross-reference business. As you might have gathered by now, I've spent a pretty significant part of my career working as a product manager for B2B products, which is why the topic today is especially very close to my heart. Now, what can you expect as outcomes of this webinar? Essentially three things. Firstly, we'll try to understand what is it about B2B product management that makes it so unique and different from B2C products. Secondly, we'll try to understand what are the skills needed for B2B product management and is it even the right fit for you. Thirdly and lastly, we'll touch upon what are the little things that you can do to take your B2B product management skills to the next level. How can you scale your skills? In the first section of the webinar, we'll try to uncover and answer the first two questions. What is it about B2B product management that makes it so unique and is it even the right fit for you? To answer this question, we'll go through the customer journey of a B2B product. We'll try to understand how is it different from the customer journey of a B2C product and also the skills that are necessary for a B2B PM in order to succeed in each stage. In the interest of time, we'll not cover the entire lifecycle in a lot of depth. We'll only try to understand the most prominent differences between B2B product management and B2C product management as it relates to this lifecycle. Alright, so let's get started. We'll begin our analysis by looking at the consideration and evaluation stage of the lifecycle, where essentially the customer is out in the market looking for a new product and at this stage the customer is evaluating the different options available to them. At this stage, what makes B2B product management so unique is the concept of the user versus the buyer persona. To better understand this, let's talk about Spotify or Netflix as an example. Who is a user and who is a buyer for Spotify? As a Spotify user, I am the buyer meaning I pay for my Spotify subscription out of my own pocket and I'm also the user. So it's safe to say that for most B2C products, the user persona is also the buyer persona, but that's not always the case for most B2B products. For B2B products, the user persona is typically the end user who is also most focused on the operational and tactical excellence and ease of use of the product, whereas the buyer persona is usually somebody more strategic, somebody who's more interested in more higher level strategic goals like return on investment. Is this product going to help my company save time, save money, make money? So essentially a successful B2B PM understands that a successful product appeals not just to the end user but also the buyer persona. And so a successful B2B PM is able to prioritize problems and outcomes that alleviate concerns of both of these different personas. Next is the purchase stage where the customer is actually in the process of purchasing a new product. Here there are two very essential differences that arise between B2B and B2C product management. The first is the concept of ACV or average contract value. And the second is the presence of a sales team. Let's tackle them one by one. What is meant by ACV? ACV refers to average contract value or the average value of the average monetary value that another business is paying to your product or to your company in exchange of your product or your service. The B2C equivalent of this is average order value or AUV and how you can better understand that is by understanding essentially the cart value when you're checking out or buying something off of Amazon or any other e-commerce platform. Generally speaking, ACV or average contract value of B2B products tends to be much, much higher than the average order value of a consumer product. It usually runs in millions, which is why number one, there is usually a sales team present for most B2B products which is responsible for converting new customers, new leads to potential customers. This is also the reason why the sales cycle for B2B products tends to be much longer. And this phase also is highly evaluative and competitive because your customers are really evaluating your products against your competitors to finalize the product which has the best return on investment. A successful B2B PM understands that it's very crucial to support the sales team during the stage and so a B2B PM makes extra effort to ensure that they understand the sales process how leads are generated and move through the pipeline and the crucial role that sales teams play in the success of a B2B product. A successful B2B PM also educates the sales team about the clear product market fit so they help the sales team understand who the right persona or who the right business is to target for their products and also onboard them and educate them about product updates and enhancements. The next stage of the customer lifecycle that we'll be talking about today is the onboarding phase. This is the phase after which, this is the phase after your customer has essentially purchased your product and now they are getting ready to use your product. This is also one of the biggest differences that exist between B2C and B2B product management. On the B2B site, there exists a huge post sales team which are responsible for continued relationship with the customer after the sales is done. The relationship that your post sales team share with the customer is highly crucial. It's very high touch, meaning it's very hands-on and highly personalized. Usually this manifests in the form of an account management team which are usually in touch with your customer throughout the lifetime that they are your customers and also customer success teams and professional services team that ensure that your customer get the most value out of your B2B product. On the other hand, the post sales relationship of most consumer products is likely more tech touch, meaning it's a lot more transactional. Whereas in B2B products, the post sales relationship is highly high touch and far more personalized. A successful B2B PM understands that the post sales team play a very crucial role in the success of your product. They view their post sales team as a treasure trove of insights that they can get from these teams as far as understanding what's working well for the product and what's not working well for the product, what the unaddressed needs of the customers are. Next, we'll talk about the phase of the customer journey where your customer is actually using your product. This is the use and experience part of the lifecycle. One of the most prominent experiences that both B2B and B2C PMs face in this stage is feature requests coming from customers. As you can see, feature requests are common in both B2B and B2C products and your customers usually land up saying something like, we're not going to buy your product unless you build this for us or we're not going to renew our contract with you unless you improve this or you incorporate this into your roadmap. However, in B2B products because the average contract value or the ACV is so high, the feedback from your customers tends to have a greater influence on your roadmap than in B2C. And what this means for a successful B2B PM is successful B2B PMs have, again, a very clear understanding of their product market fit because if there is no clear product market fit, you keep having this leaky bucket of your customers joining and your product not being the right fit for them. Successful B2B PMs also have a very, very clear definition of the product vision and strategy that is not only well understood by their internal stakeholders, but also by their external stakeholders, meaning their customers. Successful B2B PMs also understand that decision making needs to be multi-dimensional, meaning that decisions cannot be made on opinions alone or on data alone. It has to be a well-oiled balance between the two. And of course, keeping a constant pulse on customer pain points and needs always helps because PMs are then better able to anticipate and prioritize some of these feature requests. Lastly, we'll talk about loyalty and advocacy. For your customers to be loyal to you to continuously renew their contracts with you and to be advocates for you, as a BM, you need to have a high level of user empathy for the customers of your product. However, in B2B, this developing user empathy is extremely challenging. This happens essentially because of two reasons.  What I mean by that is no two users of your B2B product are the same. They could be different on the basis of the content of the work that they do, their organizational structure, the level of engagement that they might have with your product. The second thing is that they might not always be able to readily provide their transparent feedback about your product. And again, this can be because there's a severe time crunch or because they're dealing with sensitive data and for that reason they're not allowed to share transparent feedback with you. Another thing to keep in mind is because most of the B2B products are somehow geared towards operational excellence, enhancements cannot have a steep learning curve because otherwise they tend to disrupt the workflow of your users. And so a successful B2B PM understands that yes, building user empathy requires a lot more conscious effort and product discovery needs to be done in a lot of creative ways involving different ways of research, alternate data sources, etc. Successful B2B PMs also understand that the release cadence needs to be well-paced, it cannot be too aggressive and changes cannot be too radical, they have to be iterative in nature. Customers need to be trained about big changes that are coming up, especially on cold floors. Now we're nearing towards the end of the first section of the webinar. I think it's fair to say that in summary, B2B product management tends to be a lot more high-touch, a lot more personalized, but it's also more risk-averse and more expensive as compared with B2C product management. And thus, a successful B2B product manager in summary requires these five critical skills in that toolkit, the ability to communicate constantly and clearly, the ability to prioritize effectively, the ability to minimize risks, the ability to build trust and convince smart people around them, and the ability to develop high empathy. So let's tackle the second section of the webinar where we'll touch upon what can you do as a B2B PM to scale your B2B product management skills. How we go about this section is we'll individually review each of the skills that I called out previously. And then because there's a ton of really valuable information on the internet about what you can do to take each of these skills to the next level, I'll call out that one single thing that was the game changer personally in my career. And I'll also explain why it worked for me and then what you can do to successfully implement that recommendation. We'll start with how can B2B product managers minimize risks. The best way to do this is to have a focus group of experts and meet with them at a regular cadence. What I mean by a focus group of experts is basically representatives for your product from individual departments within your company. And it's even better if you're able to include some customers into this focus group. The idea with this focus group is to meet with them at a regular cadence and have a continued discussion going on about some of the ideas, some of the problems and the solutions you're working on. Why this works really well is that your idea gets better at each stage of the development life cycle. And you're also able to build a group of advocates for your product who can then ensure that your product is set up for success and it's being built in the right way. The next skill to focus on is how can B2B PMs communicate effectively. Again, there's a ton of really valuable information on the internet. But what was really the game changer for me was being able to proactively anticipate and prepare for the types of questions different stakeholders ask you and basically be proactively prepared for answers of those questions. And what worked really well for me was a stakeholder map. A sample of the stakeholder map is already available on your screen. This exercise really helped me tremendously in anticipating and better communicating my message. The next skill to focus on is how to prioritize effectively. Again, the game changer for me personally was having a very clear definition of what the product mission, what the product vision strategy and the North Star was and ensuring that the stakeholders around me were all aligned around that common mission and vision. This helps because your stakeholders also know and understand what is important for you and then they are able to support you in executing that product vision. Next up, how to build trust with your stakeholders. The game changer here is really shadowing your users or asking them to demo to you how they use your product. This is really crucial because it really dispels a lot of notion for you as a PM and shows you how your products are actually being used by your end users. That knowledge is extremely crucial in ensuring that you make the right decisions about solving the right problems. And lastly, how to develop high empathy. For me personally, what worked really well was taking a genuine interest in how my stakeholders day to day looks like and understanding their motivations and fears. For this specific scenario, one book that really helped me tremendously was The Culture Map by Erin Meyer. I highly recommend this book because it has a lot of actionable tips and tricks in better ensuring that you're able to build a better relationship with your stakeholders and you're able to communicate and collaborate. And that was it guys. Thank you so much for attending the webinar today. I hope that these tips and tricks proved to be successful and useful to you. And I'm always up for a conversation. My LinkedIn is right here. So let me know if the conversation of the webinar today was useful to you. Thank you and have a great day.


Every day, numerous advancements in medicine help heal and improve the quality of life of people throughout the world. Many of these advancements are made thanks to research done with laboratory animals. But at the current pace at which science moves forward, researchers may find themselves under enormous pressure to publish their results, placing both the quality of their research and the well-being of their animal subjects at risk. So how can researchers keep up with the speed of science? How can they make sure laboratory animals are properly handled? How can they get the most out of their experiments? The keynote speakers at the Virtual Conference on Laboratory Animal Science, hosted by Lab Roots, may hold some answers. Faced with the ever-increasing pressure to publish results, the risk of bias is a pervasive problem among institutions, journals, and various fields of study. Dr. Malcolm McLeod describes how scientists can combat this risk in planning, analyzing, and reporting in vivo research by doubling efforts to properly report study designs, and he proposes strategies for improving the quality of animal research in general. Similarly, Dr. Katie Lidster discusses measures instituted by the National Center for the Replacement, Refinement, and Reduction of Animals in Research to improve the design and reporting of animal studies. These include the ARRIVE guidelines, a kind of scientist checklist aimed to maximize information published while minimizing unnecessary studies. The guidelines are endorsed by over 600 journals, major research funders, universities, and societies in an effort to ensure that animal studies are robust, transparent, and reproducible. While the actions promoted by Dr. McLeod and Lidster could certainly help scientists monitor some of the more pronounced sources of bias that may affect animal research, what of the less tangible kind that typically aren't or can't be measured? In his keynote address, Dr. Jeremy Turner discusses how vibration, noise, and ultrasonic noise, the kind produced by lab equipment, fluorescent lighting, and electronics found in most animal facilities act as insidious sources of stress in biomedical research. In addition to explaining how these stressors affect animal studies, Dr. Turner provides practical steps on how to minimize them. And expanding on the issue of limited measurability, the final keynote speaker, Dr. Hugh Gallage, examines one of the most challenging questions faced in conducting animal studies. Are euthanasia methods for lab animals actually humane? Dr. Gallage weighs what the most recent scientific evidence says about the humanness of various killing techniques and makes the case that the negative impacts of commonly used methods should be considered during the early stages of planning studies before the decision to use animals is made. As the foundation for the numerous discussions held at the Lab Animal Sciences Conference, these four keynotes provide a critical overview of animal research today and a forward-looking glimpse of what it could one day become.


Heat. It's all around us. It can melt, boil, flow, expand and do so much more. But what exactly is it? What are the laws that govern it? And most importantly, can we harness its power to push and move things? Welcome to thermal physics. Why care about these questions you ask? Well, because understanding heat revolutionized our technology. We went from relying on horse-drawn carts to zooming along in steam power trains. We transitioned from manual labor to operating powerful machines. In this course, we'll explore everything from how ice water can crack pipes to the heat death of the universe. Whoa. Are you excited? Let's dive right in. In the first unit, we're gonna learn the fundamentals of heat. How it flows between bodies, how quickly does it flow, and some weird behaviors of ice when it comes to heat. And then in the next unit, we're gonna double down on it. We're gonna learn about the different gas laws, the thermodynamic processes, and then use all of that to understand heat engines. And then finally go on to understand how our universe is going to end. And inside each unit, you'll find videos for concepts, you'll have practice questions to fill your gaps, quizzes, and finally unit tests to master all the concepts. So if you're as excited as I am, I'll see you inside.


And there has been a huge consequence to our efforts at combating violence in southeast Nigeria. Security forces have committed a catalogue of human rights violations and crimes under international law. The evidence gathered by Amnesty International paints a damning picture of ruthless excessive force by Nigerian security forces in Imo, Anambra and Abia states. And that's according to Osai Ojigou, the country director at the organization. They are of the opinion that Nigeria's government has responded with a heavy hand to killings and violence in that part of the country. Eyewitnesses told Amnesty International that the security forces have engaged in excessive use of force, physical abuse, secret detentions, extortion, burning of houses, theft and extrajudicial executions of suspects. The organization documented 52 incidents of unlawful killings and 62 cases of a butchery arrest, ill treatment and torture.


Welcome folks, here's the downed investors trading up 51 Nasdaqs down 11, S&Ps are off 2. Go contract up $12.70 trade in 1950oz. We have silver up 8 cents, $22.37 anoz, light sweet fruit up a buck 28. $78.45 a barrel, notes and bonds. A 10-year note, trading flat $107.13, $30.00 down 3 ticks at $113.09 and $kingdala, $kingdala, where are you down like 253 ticks. $kingdala is down 236, trade in 105, 631, Euro is out here at a price point of 122, yen's at 151, British pounds at 107, British pounds at 122. Now let's get over to the spy. So, you get the spy as well as, let's do the spy first. The spy is an ABC structure up folks, okay? Big day on Friday, took the B point out, took it out with volume, you're trading 440, that's like 462. You're taking a look at it. We take a look at the cues and cues are basically setting up the same way. You know, you took out the B point, took it out with volume, I'll give you those numbers when we start up the show, but the bottom line is that this market wants higher price in a monster way, not in a small way. If we go take a look at the 10-year note, what you're going to see with the 10-year note out here, we rejected lower price at $107 today or $107.13 and you can see that volume. See that volume contract? You've only done 1 million contracts. Now this is a big deal because what's happening here, I believe we're going into almost 3. 2.8. You're going to 2.8 and 2.7. That's what you're going into and you did 1 million. A million is $74,000 right now. So you can see this also wants higher price, lower yield and then if we get over to the dollar, would you going to see with the dollar? Now the dollar is in the higher trading range. You know, it's been given it up today, that's what gave this market a little juice out here, but that being said, in order to get in the lower trading range, we're down to $226. The lower trading range is the $105.35 and we hit $105.587. I expect we're going to get down there. I expect actually that this has been building cars. You might have an ABC structure down and all you're just building cars to a lower price. Now that being said, there is support right underneath where we are. You know, the 106, 104.699 is where you broke topside from. Stay right there folks. We'll come right back.