Indeterminate: the hidden power of 0 divided by 0

Hmm, I'd say that for all positive numbers (including 0), n^infinity would be equal to 0 for [0...1), 1 for [1...1] and infinity for (1...infinity]. Prove me wrong.

Please answer. What is N! equal to if N is infinite? A Ph.D. answered that it is "not defined". Isnt it equal to N instead?

0/0 = Chocolate. It's whatever you want it to be so I want it to be chocolate :)

I love the videos. I wish we had teachers whom could describe these things as clearly as you.

hello nerds

Actually, 3/0 = +- infinity. It depends from where you approach 3/x on the singular point x=0.

I visualize fractions as the denominator is n number of boxes, and the numerator is x number of items to split between the box(es).

Keep in mind, that infinity is not a specific number, but the value of all values, the complete opposite of zero, the value of no values. Say you have 1/0, that means you have one item to put in zero boxes. Now, try to calculate how many boxes it would take to make a whole number of items. The answer is a countably infinite number of boxes since you would need to slice the item into infinitesimally sized slices, here's why: with zero boxes, you have an infinitely small amount of the item in the non-existent box. Now, say you have an infinite amount of boxes, each containing an infinitesimal amount of the item. With that infinite amount of boxes, the infinitesimal would cancel to equal 1, making infinity the answer.

Therefore, my personal theorem is that in the case of x/n, where x is any real or imaginary number and as n approaches 0, x/n approaches infinity. The solution, and definition, of 1/0, is in fact infinity. Obviously, the analogy of using boxes is nowhere near practical to the real world, but theoretically it works fine as a visualizer.

This is some cool shit they don't teach you at university!! thanks mathologer

I want to provide that T-shirt to every human on this planet...

I'm just your average joe. I have no idea what they're ever talking about BUT I LOVE THIS SHIT

Great video, thanks so much for these.
Wouldn't three divided by zero be a different infinity then say 2 divided by zero?

can you do a video on all the "special" derivatives? you showed at 5:16 ? like we all know the derivative of e^x is e^x and if you study anything related to science it will save your behind 5 times a day. so it´d be nice to know why it does that. (why is the derivative of e^x e^x. not why does it save our southern ends on a daily basis. though that´d be a nice touch as well. i think you did several videos on e but i don´t think you actually explained why it is it´s own derivative. if my memory serves my wrong here i´m sorry) same for sine and cosine, we just know it, we learned it we accept it, but why is cosine the derivative of sine? or why is 1/x the derivative of the natural logarithm? I mean the fact it is saves our hides if we are to integrate 1/x. the good old one over alpha rule might be a bit of a problem here as we´d end up with 1/0 which is quite headache. (lost a bunch of points in my first maths exam at university there^^) but at least i never learned why it is. the only proof i´ve found on the internet was a bit itchy. i don´t remember it correctly but i remember it being a bit of a headache and somewhat jumpy in it´s logic (as was the whole dude who did it. mathematics and politics don´t have much to do with each other but a guy doing a video "explaining" why the holocoast is a hoax should definitely stay away from maths. he has his pretty own set of "logic" )

can you make some video about the principle value? integral of 1/x from -inf to infinity exists in principle value.

Huh?

well newton and litnitz founded calculus(or analasis) by defining integrals and primitives(undifined integrals)

invent or discover?