0 divided by 0

Hey guys!  There's this new video about what 0 divided by 0 actually equals, and it debunks a big misconception.  It's actually a great explanation of 0/0, and I can't believe I didn't realize that almost every other explanation I found online was actually wrong.  You guys should definitely check it out, and post what you guys think about it here on the notes.  Here's the link: https://www.youtube.com/watch?v=gK_R4eOLPq0&t=5s

0 divided by 0 is meaningless because how many times does nothing go into nothing?

yeah, it's undefined

but a lot of people say it's indeterminate, and the video actually debunks that misconception

if you have 5 minutes, you should watch it

It only takes one zero to subtract from another to get the answer.

But, division which usually count the number of subtractions needed does not work for zero, and in the case of most subrations, it does not work all that well either as the the usually something "left over".",

Yeah, that's an interesting way of looking at it.

When a child learns to count, the parents are usually very proud, But then they learn that counting is not all that useful, as they are told about these weird things called fractions.

It all gets very confusing.

can anyone explain these beasts called imaginary numbers. By that stage, the child comes to the conclusion that this whole mathematics thing is imaginary.

@mercatorproject - I've always found that there's sort of an inverse relationship between how advanced a mathematical concept is and how practical it is.

Everyone needs to be able to count integers - so fundamental. Basic arithmetic next - because it clearly has practical interpretations everywhere.

Fractions are useful too for everyone to a point, doing woodworking or cooking. You want to be able to measure that 2 1/2 cups flour if all you have is a 1/4 cup measure for example.

As I see it, irrational numbers are the first place where we mathematics diverges from the practical world. Is there any practical distinction between square root of 2 and 1.414 for most purposes?

@mercatorproject - but as far as imaginary numbers - they were first called 'imaginary' by Rene Decartes, and it was in a critical and disparaging manner. The history goes something like this:

People wanted to solve various cubic equations: x^3 + ax^2 + bx + c = 0. Some bright mathematicians found that they could find exact solutions but as an in-between step they had to take the square root of a negative - which of course is illegal if your universe consists only of real numbers. Descartes didn't like this (with good reason), so he called them imaginary.

These days complex / imaginary numbers have been defined properly and understood clearly - so the use of the word 'imaginary' is a little unfortunate, but it's hard to fight history (besides it makes a good story)

@mercatorproject - However it's important to understand that complex/imaginary numbers don't have the same physical interpretations as real numbers do. This is why they can seem esoteric - however they really are useful tools. Formulas that seem to be random make a lot more sense when complex numbers are introduced.

Ex: sin(a+b) = sin(a)cos(b) + sin(b)cos(a) looks completely random and hard to remember, but equipped with complex numbers it's easier to understand this.

Yeah, and about this sin and cos thing. You get first told that are about right angled triangles. Then they are slightly modified to explain any kind if triangle. And later you are told that they go up and down and you go round and round in circles.

You get dizzy and fall over that way, you know!

@mercatorproject

Haha! Yes. I get what you are saying.

Part of this is just history influencing the way that trigonometry is introduced. As I understand it, trigonometry used to be mostly a tool used by navigators, and in this situation, applying it to solving triangles (law of sines and cosines) was the important way to think about the trig functions. Because you wanted to find unknown distances and angles.

Later it was discovered that trigonometry is so useful to describe periodic systems, like signals and waves.

But yes, all these different topics definitely get confusing!

And don't get me started on that dx and dy business which are the things that can be shoved around very conveniently in various mathematical manipulations.

And the idea that there are gaps in the continuum, and that these gaps have a further lot of gaps.

Big bugs have little bugs on their backs to to bite 'em, and these bugs have littler bugs and so ad infinitum.

And lately it has gotten worse.

It is all part of the Mercator project which is unfinished business.

It will help you navigate in this crazy maze of clanging symbols. You ain't heard nothin' yet!

oik