I love empowering people to succeed in math. I have taught university courses ranging from algebra and calculus to upper-level probability and statistics courses. I have a PhD in mathematics with research in probability theory, and a masters in statistics. Thanks so much for being a part of the channel!
The probability one was always my favourite. I worked it out myself without first knowing a long time ago so it is special to me. Plus probability theory is up there with my favourite fields in maths.
We don't know what infinity is so what's the point of spending time on solving these type of questions or derivations? All of these are based on assumptions and no proof. We can just assume anything we want in questions involving infinity and no one can ask why you have done it like this.
There is 360° in a circle because there is basically 360 days in a year ? Like what the hell is that supposed to mean ? Same as our number system is based on how many fingers we can count on ? And no-one knows why ? So you can all just be quiet. LOL
Perks of studying computer science I guess 😂 Binary search was one of the examples to teach us about the runtime of different algorithms, also talking about Big O notation. This one was always fascinating to me as the idea is so simple yet so powerful
Nope. The video didn't make it clear that it had assumed an abysmal redefinition of 0.999.... Decimals are unsuited to representing numbers that differ from a real by a non-zero infinitesimal. For example, there would be no decimal for 1 - 0.999... or 10 * 0.999... - 9.
Riemann Sphere a world you can easily do devision to Zero: The Riemann Sphere is a mathematical construct that extends the complex plane by adding a point at infinity. This allows division by zero in a meaningful way within complex analysis. Specifically, on the Riemann Sphere, dividing by zero corresponds to the point at infinity, where operations can still be defined. In essence, it provides a geometric framework where division by zero is handled by considering limits as numbers approach infinity or are very large.
i always thought it was interesting to think of division by zero as resulting in the infinite set of all numbers. i considered this because of the breaking of the multiplicative inverse. for example, 2 * 5 =10 so we can get our 2 or 5 back from the 10 through division, but if we take 2 * 0 = 0 not only can we not get our 2 back in the same way, but we also see that all numbers times 0 is 0, so we could theoretically get literally any number back. to put that more explicitly, x * 0 = 0, so x can be anything, or x is every conceivable number; it is an infinite set. but then, i suck at math! 😅 i just thought it was a fun idea.
This could be a crazy theory, but I think all exponents start with the number 1. For example, 3^4 isn't only 3*3*3*3, it's complete equation is 1*3*3*3*3. When you perform 0^0, you start with 1, and then you multiply it by 0 0 times. Let's not forget that exponents are nothing more than short hand for multiplication. Same goes for factorials. I'd argue that if any system didn't have 0! or 0^0 to be 1, it would have to be an entirely different system of math, and the idea of math is to be one unified system of performing funtions to numbers to reach other numbers, so it would be entirely unuseful. However, Dr. Sean is way better than me at math, so I could be wrong.
My favorite representation is the Taylor's Series, because it relates e with sine, cosine, i, pi, sinh, cosh and hyperreal calculus. Also, as an infinite series you're mind blown when you see that it's derivative is really itself!
Why not create an object that has the required properties? 1/0 = &; Just like squareroot(-1)=i; Than you would have something like this: 6/0 = 6&; &/&=1; &+&=2& You just store the information that would otherwise being lost.
Using S in the arithmetic proof assumes that S exists. This is not the case. The series obviously diverges. In the Abel proof if 0<x<1 upper order addends are closer to 0, and so they are negligible and can be cancelled out reaching a certain level of precision on the result; in other words the series converges for 0<x<1. This is not the case with x=1. In other words the function we are searching the limit for x-->1 isn't continuos for x=1. Otherwise why shouldn't look for the limit for x>1 as well?
E as I use it: Exact; Equivalent; Expression (energy), e^i for 'computational cost' but the most [E]vil way I use it, as to denote exponential constant values, for scaling of base 3/4 calculation expressions into self-similar real-number ratios of irrational "digits" being operated on logarithmically.
@@AndrewDangerously It would require an exponential amount of text. Do you describe that 'amount' of that text using units derived from paragraphs? from words? from characters? From sentences? Pixel on/ off rate? The various electrical circuitry quantitues, taking their own exponential functions into account of this unknown value exponent? See, 0,1, and 2, are not real. 3 is where the real value baseline begins, as far as the instructional code for reality. 012 is a *continuum constant* that acts as a function instructing relative operational order of value exchange between real quantities. Dimensions aren't real. Yet trigonometry is extremely correlative to the deep-scaling of that very concept. Idk what to call my theory yet, but seems to be very well supported by every stone I turn over in my expansive search.
@@AndrewDangerously Uhh. I tried... So 1^2 is 1. Terrence Howard really screwed me on this shit ngl lol.... but he's crazy. And I'm both/neither. He is onto something deeply irreducible about the discrepencies of '1', '0', and 2; to the exponent of the discrepancies from using -=X/ as our 4 highest order "math operations". 1 is actually an irreducible scale unit that represents an infinitely irreducible and unique value composed of higher and lower order integral values as they are ALL, mutually calculated. In %base10linear: 1=sqrt(-2)
Terrence has glimpses and he's high EQ, he knows what he saw, and he just runs with it. But he has no idea wtf he's talking about it what it actually means, or when and where to actually appy it without sounding like a snake oil salesman.
