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Hey. An engineer here. I'm sure there are mathematicians here who have a better grasp on these concepts. When I see such a title I was expecting an example where using dy/dx as a fraction would make things very messy and wrong. That's not what you did. Someone gives us an example where considering dy/dx a fraction is "a sin" 😅.

It’s a section of the cotangent bundle and should be treated as such

0⋅∞≈0⋅x/0⋅∞⋅0÷0⋅∞÷0÷0-0⋅∞

“The Genius of Srinivas Ramanujan”🙏🙏✨

1:49 that r is still stuck inside of that ln

X^1/0=?

x + h - x = dx [horizontal] f(x + h) - f(x) = d f(x) [vertical] d/dx f(x) The ratio stay the same, since we scale the distances equally

This is why the division by zero is not permitted

The term 'dx' indicates a small change in x (or that x approaches zero), and the term 'dy' indicates the small change in y caused by that dx. Now the derivative is just the small change in y divided by the small change in x, dy/dx.

0⋅∞=undefined

d^(2*y)/(d*x^2)

(1+i)/√2

Pattern seeking brain approves

0

at 0:07 you make a mistake and say 117 instead of 177

Liked and subscribed! Can't wait to see more content like this! 😊 Keep up the great work! ❤

Bro any olympiad aspirant can solve this without opening his eyes .Now understand what is the level of question/////??????

It can actually be a fraction of hiperreal numbers

*0 ÷ 0 = Undefined.* ... It's an existential dilemma

Great vid man😊😊

Its -infinity

Nice loop!!!!

you had to ruin it by using stupid notation

dy/dx=lim(y(x+h)-y(x))/h,h-->0)

You might know it as... I DID NOT KNOW IT AS THAT.

Can you say which mathematics degree is a better choice in the long term: Mathematics(regular) vs Applied Mathematics?

Also known as an infinite geometric series - S(∞)=t1/(1-r), where -S(∞) is the sum of a series till infinity -t1 is the first term of the series (in this case 1/2) -r is the common ratio between numbers in the series (in this case, also 1/2) The series shown in the video can be represented as S(∞)=(1/2)/|(1-1/2)|, or, (1/2)/(1/2), then subsequently (1/2)(2), which equals 1 Here, for the people who see this comment, try it with the series (2/3) + (4/9) + (8/27)... and reply with the answer if you feel like it.

It's called Zeno's paradox!

Naw the answer is π²/6

At 01:40 you are doing it in a wrong way.B+B=2B=Lim n->♾️ {1-1+1-1+1-1....+[(-1)^(n-1)]×n} You are hiding that last term and neglecting it

))) One divided by zero is infinity. But two divided by zero is infinity twice.) Everything wooorks.....except.... For it to ultimately work....somehow zero and infinity have to cancel each other out upon being multiplied by one another.

i use dot/dots above

yawn..classical case of swapping the prerequisite of the proof with the result. You can't put a sum to a diverging sum and then say, that it doesn't diverge because it has a value.

Not so amazing. This is called domain extension. In the normal world 1+2+3+.... = infinity, just as you would expect.

Infinitieth root "x^1÷∞" is littearly a 1 maker

5:40 but if you are saying that we don't divide by 3 to continue the pattern instead we multiply 1 , 3 less each time then how would you define negative exponents? You pattern will just stop as 3^0. So the pattern indeed continue by dividing by 3 so that all the properties of exponents continue to work for all kinds of exponents. So 0^0 is indeed undefined but we use 1 for certain contexts because it just works fine over there.

how can we decide its length be 1??

people say that the paradox is we would need infinite amount of let's say a paint (not caring about the size of atoms here) to paint the surface but that just doesn't make any sense like what do you mean by "amount" here in general we consider volume as the "amount" in day to day life. So, suppose if I ask to paint a even square of side 1 meter what "amount" of paint I need. Do I answer lm^2? That doesn't make any sense we always mean volume when we say amount do we can't say you need infinte amount of paint to paint an infine surface. As we mean "amount" as volume so suppose there is an infinitesimally small thickness of paint over the infinite area so the amount of paint will actually be " the infinite area times the infinitesimally small thickness" and that as you said CAN result in a finite volume so an infinite surface area can be painted in theory by a finite volume. and this logic fits here perfectly as the as x approaching infinity the layer of oaint in becoming very thin and thin thus becoming infinitesimally small

It's also nice to look at in binary number system: 0,11111111...

1:25 the illegal moment.

e-1 i guess 😅

\| 2pi = 2,5066282746

e

I just want one video to openly admit, without being petty or pedantic, that it is because we had to define it that way to make things work. You said you would show it in a more mathematical way, but you really didn’t. You just put math in the background and said “well it has to be for this pattern to work.” If you wanna use the semantic argument, it’s just as easy to say there is no way to order nothing, so there are 0 ways to order it, rather than saying not ordering it is a way of ordering it.

I think 0 x ♾ is 1 if your using limits. The examples in the video with limits had the sides unbalanced, and they approached their goal at different rates. If we make a limit that has sides at the same rate you get 1 limit x -> ♾(1/x) * x (1/x) * x = x/x = 1 If you have nothing and everything at the same time it makes sense for it to be 1 If you aren't using limits I would define infinity as 1 + 2 + 3 + 4 + ... 0 * (1 + 2 + 3 + 4 + ...) If you use the distributive property it becomes (0 + 0 + 0 + ...) which is 0

it feels like your being the friend whos there for me when no one else is. Much the same to math.

great vid!

E(2)=2