Can math notation be improved?

Those aren't reals.

A bijection between the naturals and the reals cannot exist.

What are you smoking?

[math]\pi \mapsto \tau[/math], for Turn

Drop arabic number symbols for symbols that hint at the cardinals they represent (e.g. "4" being twice as much as "2")

Implying "integrate" is a good word for what's being done there in the first place

>π↦τ, for Turn
Yes

>Drop arabic number symbols for symbols that hint at the cardinals they represent (e.g. "4" being twice as much as "2")
That's a little far fetched unless you want domino dots, decimal is going to cause problems either way. I think we should use prime factorizations more often but meh.

>Implying "integrate" is a good word for what's being done there in the first place
What would you suggest? Not him, but I thought "transfinite sum" but it's not the greatest.

iirc my prof said those are not legitimate notations (for all, there exist) but mathematicians are lazy fuckers so somehow somewhen everyone just agrees to go with it. o it's probably because for each is not used enough?

Seriously, how are they different?
I'm not saying they aren't, I'm saying I can't think of a situation where they are different

are you saying that the reals actually have a bijective relation with N. It's just that we haven't discovered it yet?

>Do you recall how you would say when you're talking about a single element versus all elements?

You'd use the backwards E thingy my man.

You know... the negation of the 'for all' statement.

>Implying "integrate" is a good word for what's being done there in the first place
It's just an example of the proposed notation. Also the beauty of it it that the notation is modular so it only has to describe the operation being performed on the arguments. You could call it InfinitesimalSummingThingy(Start, Stop) if you really wanted.

yes, precisely.

don't listen to those nerds:

· I V N W H
will already be simper to learn than
0 1 2 3 4 5
for five year olds.

I always thought the Newton differential notation would be good for inverting.

I.e. 5˙ for 1/5 and double dots means you can remove them again.

And of course, base 12.

And x.f instead of f(x), so that with a function h you may map e.g. x.f.g to x.f.g.h, etc. and just add stuff when it changes