0 divided by 0...

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Provided one reaches k'th derivatives of the original functions for which division makes sense.

ruveyn

I've thought of it like an infinite sheet of dough.

If you divide by zero, the sheet remains unchanged. Divide by one, and while it becomes whole, it is not the sum of the total infinite product.

But the empty set is a subset of nothing because it is a subset of everything.

I'm glad people are thinking about this, even non-math people like YT. It's good to roll around ideas in your head and think about them. Most people tend to accept math as something inscrutable and with great authority.

When you divide by zero, there are only three realistic options. The answer could be 0, 1, or infinity. None works, which is why math leaves division by zero undefined. Notionally there are different ways to look at what it means to divide by nothing, but since none of the approaches actually works, it doesn't matter. (You could say division by zero is 0, because you've done nothing; you could also say it is 1, because you haven't divided anything; or you could say it's infinity because you have divided something as much as you can.)

Since 0 times any finite number is 0, 0 cannot have a multiplicative inverse (or reciprocal). So dividing by 0 is out, otherwise a contradiction would be introduced. That contradiction would be 0 = 1 which is just plain false.

ruveyn

And all clocks here go counterclockwise, too.

Also the moon looks upside down in the Southern Hemisphere. That is because all you guys are hanging upside down.

ruveyn

Division by zero is a big no-no. Anyone who thinks 1/0 = ∞ has no understanding of infinity - it's much stranger than that. Look up HIlbert's Hotel for some interesting effects!

The reason 1/0 is undefined is because it's nonsense. Division is not a function in and of itself, but the inverse of another function (multiplication).
When we ask "what is x/y?" we are really asking "what is z where z*y=x?" For any value of y other than 0, there is an answer to this puzzle. What is 8/2? What is z when 2z=8? z=4. What is 1/0? What value is z when 0*z=1? There is no value for that. We all know that 0*z=0 for any z.

Absolutely!

In Australia you buy expensive and sell cheap in order to make a profit! And your boss will refuse to give you longer hours with less pay unless you go on strike!

They age backwards there too!

i understand what you mean.

in a strange way, everything is composed of nothing. it boggles quantitative arithmetic views of reality.

a "point" is a location of a singular element of space, and it has no volume because it has no dimensions on any axis. it therefore could be said that a point does not exist because it has zero size.

but the universal spacial volume is composed of individual points of space that can not be said to exist since they have zero volume.

in some ways i can conceive that it should take infinite acceleration to even depart from inertia considering that any velocity that starts at "zero" (with respect to the inertia of the subject at the beginning of the acceleration event) must make an infinite leap in velocity from "0 points per second" to "infinite points per second" before they can even be considered to be "moving"

the shortest distance that could ever be measured by the smartest life forms in the universe is nevertheless an infinite points long.

i can debate with mathematical knowledge i have (that i have learned from books), but i prefer to consider the ideas of "infinity" and "nothing" in a more philosophical sense. i do not want to enter an "i know more than you" altercation. i am not interested in academic debate. i never have been.
i am interested in personal considerations about the compilation of reality that are not strangled by peoples ideas that only the select few can ever think it through.


when i was young, i always wondered what was more powerful. infinity or nothing?
is an infinite amount of nothing bigger than a zero amount of everything?

i guess it is. an infinite amount of "nothing" produces "something" which is greater than the "nothing"
that is not multiplied infinitely.

a point multiplied by infinity (or given an infinite value) will give rise to a line, but a line does not exist either because it has no breadth or height. it only has length.

an infinite amount of lines are required to produce a plane which also does not exist. planes have no height so their volume is zero.

an infinite amount of planes are required to produce volume which does exist.

it is all composed of nothing however and that is the point.

I understand the concept fine. That actually does make sense in the context of limits but one must just not make the mistake of thinking that infinity is a multiplicative inverse, which it isn't.



Consider the function f(z) = 1/z. Then lim(z -> ∞) f(z) = 0, lim(z -> ∞) z = ∞ and lim (z -> ∞) f(z)*z = 1.

One could also find functions where the form 0*∞ could approach any real number though. So algebraically, infinity cannot be a multiplicative inverse, nor can it have one.

You do understand the concept, Jono - this is clear from your use of limits! Infinity is not a number but a concept - this is where most laypeople fall down, as they often think "infinity is the biggest possible number".

In the hyperreals infinity is a number (sort of) but it does not have the algebraic properties that standard real numbers have.

ruveyn

I'm not sure that there is a specific algebraic definition of "number". However, although it is possible to extend the set of real numbers to include infinite and infinitesimals, like what the hyperreals do, that set can no longer have algebraic properties required in order to be called a field.

If you talk to laypeople like that, you'll just end up replacing one misconception with another. The honest answer is that the word "number" is not actually a technical term. It doesn't matter at all whether infinity is a "number" or not. What matters is that infinity is not in R (the "number line") but is in R-Bar (the "extended number line").

Straight from Euclid:

Σημεῖόν ἐστιν, οὗ μέρος οὐθέν.


ruveyn