Great teacher vibes

Great! - I thought i could hear him thinking :) - btw at 9:00 i already knew that the calculation simply fits in aby base similar or higher than the one in which it has been typed into :) - what about unary base and 2,7182818281451(...) bases? are we getting there in this episode :) ?

My man ventriloquisming.

@@maynardtrendle820 shh don't tell the chickens that you know.

My goodness, the gall to suggest a non-triangular number as a base. Do you think we are heathens?

​@@OMGclueless We are Babylonians! Knuckle counting ftw!

@@gljames24 Wasnt it egyptians? Oh ok - 60 = 12x5 :) true - these were babylonians, the 60th people :)

@@OMGclueless It's twice a triangular number, that's still pretty good.

Your bases may be anti-primes, but they're not _simultaneously prime._ This message brought to you by the only superior-highly-composite base that isn't a composite base. And also counting to 7 with only 3 fingers.

funny

How can base 1 exist?

There are 2 kinds of bases, ones that have a 0 and ones that don't. Base 1 cannot have a 0 so it is just a number of 1s that add up to the number (i.e. 1, 11, 111, 1111, 11111 etc)

“Hmm what an interesting way to use base 1”

I guess Roman numerals are a "shorthand" or "compressed" form of base 1.

Quick youtube tip: You can pin your comment so that it ends up at the top and more people will look at it.

Quick youtube tip: You can rename your channel ComboAss so that it ends up at the top and more people will look at it.

You did some of that to good acid and started counting with the beings from the other dimensions. It's all good, fam... I been there...😂 But you sound more fried than those chickens gonna be! You have some mathematical approaches I have never seen or heard of before, and I am still trying to gather if they have any kind of applications to things like the prime number theorem... but you're without a doubt a high-caliber prime number personality! 😂 All that being said, I can't help but feel like this is pound for pound how crazy and off my rocker ima be/look like to everyone in another yr or 2 of picking appart this theorem and trying to start my own channel. But numbers make you crazy like that sometimes... But don't take these statements in offense, I mean the exact opposite, in fact! I admire anybody who is trying anything other than the traditional 2 dimensional basic white bitch mathematics that we have now. Cuz you can't solve the unsolvable by applying the already applied techniques (or else it would be solved already 😅) But I would like to learn some of your "unconventional" techniques in a lil more detail as I love nothing more than understanding any and all approaches that can be mathematically acquired. As long as the axioms are there, of course. I plan on starting my own channel here soon, and before I do, I would like to collaborate with some "out of left field" style mathematicians who are open to new and innovative concepts like your own. So I offer you this, a short meet and greet over Skype or whatever other video platform to allow us to discuss topics and exchange information with each other and collaborate in order to further expand our knowledge and understanding of the seemingly infinite realm of numbers! This is an PŔĮMĘ opportunity to explore a whole new realm of mathematics that hasn't been discovered or applied to any conventional mathematics currently known or used. I have spent my life running numbers in different ways but have recently made a mathematical breakthrough that has broken the paradigm of mathematics itself. I can show you some of the hands down CRAZIEST SHIT that you have NEVER SEEN DONE with numbers and mathmatics! 💯 I have managed to create a full-blown new mathematical technique I have affectionately dubbed !§ỲMMẸTŘÝ{}MÅŤĤËMÅṬỊČ̣§¡ led by a paper trail of hints and tricks left by the great NIKØLÅ TESLÅ himself I have done more things and made more strides in the last year than almost any high caliber mathematician would wish to learn in a life time and I am getting ridiculously close to solving the prime number theorem itself! Fuk wit me, though! See if I don't have the techniques to multiply or divide by 9, 99, or 999 without using any multiplication or division, see if I don't have custom created PNG (prime number generation) equations that you never heard of or seen and be the first to see the prime number matrix code in action! 😎 The answer to solving this riddle isn't in the mathematics itself. It's in the laws and properties of the numbers that each one adheres to that defines what they do! The sequences and patterns, there's ABSOLUTELY NOTHING THAT IS RANDOM OR ASYMPTOTIC ABOUT THE PRIMES! THERE EXIST A SYMMETRY IN THE ASYMMETRY THAT NOBODY SEES! But you have to understand numbers in 3rd and even 4th dimensional concept (just ascended to the 4th dimension) that most will never even believe can be achieved. But I think you might be crazy enough to catch on! 😅 This is a PRIME opportunity to expand your knowledge far beyond the reaches of conventional boundaries! Do you take the red pill? Do you wish to see the matrix? Fuk, I sound crazier than you! 🤪🤯

And I already checked my numerical sequences on the online encyclopedia of integers. Nobody to date has submitted these sequences...

Hold on to your hats! Combo Class' mom just let out of the backyard!

… said the man who was bitten by a snake

Actually nature killed me in a horrible accident 10 years ago

These are exactly the equations where the base is greater than the greatest coefficient in the expanded polynomial form.

Thank you for sharing this observation. I was super excited about being able to use solutions to multiplication problems I already know to easily construct polynomial expansions, but quickly found it didn't always work and I had no idea why. For example, 13*13=169 matches (x+3)²= x²+6x+9, as expected. But 14*14=196 doesn't work, as (x+4)²=x²+8x+16, not x²+9x+6. You can kinda cheese it by saying the 9 is really 8+1 and "donate" the 1 to the 6 to make it 16, but this discrepancy only got bigger and less transparent as I used larger constants. But lo and behold, I overlooked that the starting equation must be one of those so-called "digit equations" that remains true in every base above or equal to some minimum base B. For example, 12*12=144 in any base 5 or higher; in base 4, 12*12=210 still represents the same _quantity,_ but those specific digits won't work for the expansion of (x+2)². As you pointed out, at least according to my understanding, it should be the case that for any expression using only strings of digits and multiplication and addition there is some minimum base B, where for all bases ≥B the solution to the expression is represented by the same string of digits. That's when I had the brainblast. If all expressions have a corresponding "digit equation" when the base is high enough, perhaps 14*14 _would_ encode the coefficients for the polynomial expansion of (x+4)² if I used the right base. As it turns out, 14*14 is 18g (yes, the digit g) in any base ≥17, making our _expected_ expansion x²+8x+g; g is the 17th digit in base 17, and so by itself represents *_16._* Holy sh*t it, works. The base simply needs to be large enough to represent each coefficient/constant with a _single digit_ For good measure: we know (x+5)²= x²+10x+25. However, 15*15 does not seem to equal 11025 in any base; but what the expanded polynomial is actually telling us about the "digit equation" isn't which specific digits to use, but rather the specific _quantities_ that must be represented by a single digit. I need at least base 26: 1x²+10x+25 tells us that in base 26 or higher 15*15 should always equal the _first_ non-zero digit (1), followed by the _tenth_ non-zero digit (the digit a), followed by the _twenty-fifth_ non-zero digit (p). And if we check, it is true that 15*15=1ap in base 26 and up. And inversely, while say 28*12=336 in base 10, to write the digit equation now we know we need individual digits for whole quantities up to 8*2=16, i.e. at least base 17. I've found that 28*12=2cg in base 17 or higher, so without doing any work I'm going to guess that (2x+8)(x+2) = 2x² + 12x + 16 (c=12, g=16); and I have just enough experience with polynomials to know that's correct intuitively. As far as I can tell, this should work generally for polynomials of the form (ax+b)(cx+d), where a, b, c ,d are positive integers, and you choose base B such that B>a*c, >(a*d+b*c), and >b*d. The answer to a||b*c||d in base B should always be the digit equal to a*c, followed by the digit equal to ad+bc, followed by the digit equal to b*d. One last test. I can expand (8x+2)(2x+3) to 16x²+28x+6. This expansion tells us that in base 29 or higher, 82*23=gs6, or a concatenation of the 16th, 28th and 6th non-zero digits. Double checking online shows I'm right 🎉🎉 Pretty sweet. Now if I ever don't feel like expanding a polynomial manually I can just figure out its corresponding digit equation. And for any polynomial I know the expanded and factored form of, I can very easily produce an interesting, _seemingly_ hard to calculate equation like "In base 29, 82*23=gs6". I'm not that smart to be doing multiplication in base 29 bro 😂 but I can still reach that answer with absolute certainty, and that's FIRE 🔥🔥🔥 LES GO MATH

​@@MeNowDealWIthItBrilliant reduction. Though there isn't any functional difference in our interpretations, I resolved these as the equations where each coefficient/constant could be represented by a _single digit._ Obviously, as you said, for that to be true the base must be at least m+1, where m is the greatest coefficient/constant factor of the expanded polynomial.

@@seventoast It follows that this is true of Division and Subtraction if there are no cases where a coefficient "crosses the mag barrier" by decreasing below an exponent of the base. That is, 3-2=1 is true in any base >3, as is 53-21=32 etc etc, but as soon as you have to "carry" a digit it stops being true (10-1=nine, where in any base you must switch nine for "b-1"). Likewise, 4/2=1, 44/2=22. 9999/3=3333 are all true in any base which can make sense of them, but 12/4=3 is not always true; 12/4 crosses B^1 when you calculate it, which is part of the reason it's not always correct. This is prima facie true because it is the opposite case for the addition/multiplication (ie, if you can write 1+2=3 then you can write 3-2=1), but I've unfortunately given a narrower case which has exceptions: Although you can write 121/11=11 in any base that understands it, as it follows from the similarly true 11*11=121, writing it contravenes the "crosses the mag barrier" rule. I think there's no easy way to prove that divisions like these will work without knowing the multiplication will work, as what you're conceptually saying when you say that 121/11 is acceptable is that b+1 is a factor b^2+2b+1, which is a harder thing to calculate than expanding (b+1)(b+1). 12/4=3 does not work because 3*4=C; the coefficient you're dividing in 12/4 must be "twelve" and not "12", but I can't see a way to calculate/state that without reasoning via 3*4=C.

As we let the base approach infinity, every number in the eqn consists of a single digit. That will indeed always work for that base (or higher) without carry. Duh. 😉

Exactly who I thought of, too!

Seximal base is also perfect when using D6 dices with dots on. And Combo class has a lot of those

there's also "a better way to count" which made a response to the seximal thing saying we should use binary

You can take the square roots of numbers in base 2. And you don't have any multiplication tables, its all algorithm.

@@ArchieHalliwell i love that video, especially since i already had a soft spot for binary prior lol

6!? base 720 is way too big for it to be usable.

For a transition to happen is necessary all of us base twelvist to come up with different digits and names for those new digits

base 2 🙌

​@@tafazziReadChannelDescription They've already been named as dec, el, and do. A 180 degree rotated 2 and 3 are the best proposed symbols for dec and el, sometimes dec is an X from Roman numerals, but that becomes a mess with established variables.

Many societies had a base 6 by 10 system, and even Britain had a 120 system for money for a long time. Ours is really more 10 by 10, because we use the 25 times table for a lot of things; for example, most countries use a quarter of some sort, which doesn't work with base 10, since then it would be a 20 unit coin. 120 is better than 100, because it's divisible by 2, 3, 4, 5, 6, and 8. Sadly, it didn't happen, so we have to deal with the annoying thirds all the time that never fit in well with our numbers.

@@litigioussociety4249 if you add 3 digits to base 10 you get base 13

So I'm following, this implies that there are some equations that could exist with base e but not some finite base? And visa versa

Computer scientists already abuse the hell out of big O when they say f(x) = O(g(x)) when they mean f(x) ∈ O(g(x)), or even O(f(x)) = O(g(x)) when they mean O(f(x)) ⊆ O(g(x)). That’s much more infuriating to me than what you’re doing.

Wow - you're from siberia - but from tajga? or tundra? Are there any polish "repatrians" that were sent there hundred of years ago?

@@TymexComputing I'm from Novosibirsk. There's mixed forest here. The weather is not bad enough to use it as a punishment so I believe all that people were much close to the North. It's -30°C..+30°C most of the time here and the air is pretty dry.

My favoroute is not mentioned here - its 0+0=0 - you dont even need a base for that equation :)

Isn't 6210001000 self-referential in any base >6?

@@connormeredith3144 No.

My 50 y.o. friend recently started talking to me, that when he was a teenager he was thinking about negative and fractional bases and trying to talk about it in class at school - the class wasnt happy about thinking :) and adding anymore. He ended up as a data recovery specialist multiplying hexadecimals for living.

11 yos who love different bases unite!

ps that's a compliment

Chicken! :D

so if you are looking at decimal, any multiplication involving numbers whose digits are only 0,1,2,3 will work in all higher bases

this is a stronger condition than you need. really it is about nonnegative integer coefficient polynomial multiplication in which none of the coefficients in either the factors or the quotients will be as big as the base you are using

base 10 your favorite base?! so basic and non quirky, mine is base 7 (septenary)

@@guillermo3412 septenary is base 10

@@theneoreformationist septenary literally means base 7 which means you’re utterly wrong.

@@guillermo3412 If you were using septenary, the symbol "7" is meaningless. The correct name for the base number is 10.

@@theneoreformationist i see what youre doing and again, youre wrong, septenary refers to 7 in base 10, you cant use the number expressed in the base itself to represent the base youre using, because it could literally be any number and its not useful information at all, thats why we universally use base 10 to express the base of a number.

jan misali baseless base names moment

They probably just converged, it's pretty much universally acknowledged in math circles that, as far as humans specifically are concerned, only 6 and 12 really make sense as "superior" bases due to being in the "sweet spot" of being neither too large nor too small and due to having a lot of divisors. Whether you prefer one or the other is a preference thing really - do you value the convenience of fewer symbols more or the density of a larger base?

Special accent marks can be used, like à would be a+26 and è would be e+26

The traditional way is to represent each "digit" as multiple digits of a smaller base. If you look at a digital clock with seconds, you can see 2 sexagesimal digits separated by a colon (along with either a dozenal or bidozenal digit). Each of those digits however is written as a decimal digit and a seximal digit. This is actually exactly how sexagesimal was represented in the past, though with each of the sub-digits also being represented in unary, with 1 symbol for one with 0 to 9 copies, and 1 symbol for ten with 0 to 5 copies.

There wouldn't be a zero, we don't acknowledge it these days much, but the jump from "natural numbers" to "abstract numbers" that can't be physically represented in the conventional way (How do you have 0 of something? How do you have -3 of something? etc...) is quite large. All cultures we're aware of had to first define a number system and only then, after indulging in mathematics for a while, would they realise that 0 too is a number - hence why all counting systems, be it our base 10, sumerian base 60, mesoamerican bases 5 and 20 and so on..., seem to be "off by one" You can even see this in the way people use their fingers today, if you ask a random person to show you that they have zero of something, they are more likely to show you an empty hand or shrug rather than curl their hand up in a fist (though it gets exponentially more likely if you ask for a natural number first, after that they'll just subtract the fingers)

@@asd-wd5bj it's quite easy to have zero of something. I have zero maidens

Erratum : The n line of Pascal triangle correspond to the n-1 power of n

Base 1!

#metoo !

Are you acknowledging base 64000000