Can math notation be improved?
>>8181209
Yes, the current notation is shit and difficult to understand for people new to it. Notation should give hints to what it's underlying symbols mean. I think we should all take just take a hint from programming and use natural language followed by an arguments list. E.g.
Integrate(LeftBound, RightBound)
Union(Set1, Set2)
>>8181342
>notation
>art
what
>>8181209
yeah, computers
hover mouse over notations, get explains
yes, why is there a FOR ALL but not a FOR EACH
someone make it already!
>>8181209
yes. if you would find a convenient notation for reals, i.e. easy symbols for expressing 0.00...001, 0.00..002, etc.... it would revolutionize mathematics because you could map bijectively all naturals to reals
>>8181348
Are you out of your mind? Fuck typing all that shit out.
>>8181367
It's better than huge LaTex commands.
>>8181360
How would a 'for each' be used differently.
In my opinion 'for each element in A' is literally the same as 'for all elements in A'. Looks like someone has been getting too much into visual basic.
>>8181365
>expressing 0.00...001, 0.00..002, etc....
Those aren't real numbers. Those aren't defined.
>>8181365
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")
>>8181348
Implying "integrate" is a good word for what's being done there in the first place
>>8181396
>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.
>>8181360
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?
>>8181360
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
>>8181365
are you saying that the reals actually have a bijective relation with N. It's just that we haven't discovered it yet?
>>8181407
>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.
>>8181396
>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.
>>8181400
· 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
>>8181209
I think Reverse Polish Notation should be the standard. When you or a computer goes through an arithmatic problem following BODMAS what you're doing is converting to RPN, so everything would be simpler if it just started out as RPN.
When you see 172 - 256 * 18 you know you've got to type 256*18 into your calculator then subtract that result from 172. It would make more sense if you could just read the numbers and operations from left to right.
>>8181443
this.
I always hated that you read composition of functions from right to left. its not natural in a way
>>8181209
"sin/cos/tan x, squared" notation is misleading for a start.
>>8181348
/g/fag here and I agree
>>8181209
No, because the people who teach it won't teach it any other way.
