Calc I

>the slope of y=2 is undetermined because it's impossible to tell if it's positive or negative zero

That's not what undefined means

if there are no solutions just imagine a number that would be a solution like sqrt(-1)=i

discover all the properties of the solution to 1/0 then get your fields medal

300k starting

maths

He sounds autistic.

The slope is undefined because the definition of the slope, is a change in y over a change in x.
There is no change in x, sooo it's not defined.

Seems like a computer scientists to me
>missing function
>undefined symbol
>not initialized integer
>undetermined variabile

"Undefined" is exactly the right word for it.

A relation [math] S \subseteq X \times Y[/math] is undefined at [math]x \in X[/math] exactly when there is no y in Y such that S(x, y) holds. In Hausdorff spaces, limits are unique but they don't always exist, hence the "limit function" can be undefined.

Question: in what kinds of spaces do limits always exist?

Singleton sets?
with the obvious topology

If we were to allow an infinite slope, then there would be its negative version too. These would both be vertical lines, and thus indistinguishable from one another.

but a calc 1 teacher is also supposed to make people appreciate math more, but I agree he could have phrased it more rigorously.

We allow zero slopes without this problem at all.
Personally I think infinity has a place as a number alongside/counterpart to zero. Much as it took a while for mathematicians to come round to accepting zero as a number the same seems to be the case for infinity :(

0=-0

0 doesn't, you fag

Your professor is a moron but that's expected because he's teaching calculus.

This defining x=1/0 is not the same as the defining i=sqrt(-1)

The identity i*i = -1 is actually pretty comfortable and fitting with the algebra of real numbers.

Now imagine you set 1/0 = x
then x*0 = 1 by the rules of division

-1 * x * 0 = -1
x*(-0) = -1 since multiplicattion is commutative and associative
but -0 = 0 so now you have
x*0 = -1

so x*0 = 1 = -1

immediately contradictory.

I mean, I am not saying you can't. I am just saying it is useless.

two words: projective space

>0/x=0
>x = undefined, because all real numbers work
what?
no lol hahaha

0/x = 0 is well defined for any x for which a multiplicative inverse exists.

dy/dx = dy/0 = infinity

its magic, I dont gotta explain shit

Let x*0 = +-1

wow that was hard

the problem comes from improperly defining 1/0 = x.

0 is a number which has the property of being its own negative. 0 = -0.

By extension, x is also its own negative. -x = -1/0 = 1/-0 = 1/0 = x.

0*x produces another number which is its own negative, say "y". If 0*x = y, then -y = -(0*x) = -0*x = 0*x = y.

There is no contradiction. Your arithmetic is just wrong.

It's true of indiscrete spaces too, though. Is it true of any others? I managed to show that any such space is connected:

Assume we have U != V open and disjoint. Then pick x in U and y in V. If the sequence x y x y x ... converges to p, then p is in neither U nor V.
Therefore, any space where limits always exist must be connected.

It's so jarring seeing actual jokes on Veeky Forums. When did we switch to post meme humor?

Take your pure math back to

He's one of those guys that believe math is discovered.

Are you talking to me?

Is 0 a real number?

You might as well call those anything, but using different jargon just becuase you don't like the established jargon is stupid

You might as well call asymptotes stupid.

You might as well call your prof stupid.

ZFC