/sci/ - Science & Math

[Anonymous No.1535412]

Why are addition and multiplication commutative, but not exponentiation?

[Anonymous No.1535430]

> assuming real numbers
Hey, wats a matrix???

[Anonymous No.1535435]

5 ^ 2 = 5 * 5
2 ^ 5 = 2 * 2 * 2 * 2 * 2

[Anonymous No.1535459]

>>1535412
Because if it was, you'd be here asking why they are all commutative

[Anonymous No.1535473]

>>1535412
Because God says so.

[Anonymous No.1535480]

Wait until you find out it isn't distributive, either!

[Anonymous No.1535582]

I think we need to fix this. Let's redefine exponentiation.

x^y = ((x+y)/2) ^ ((x+y)/2)

This matches normal exponentiation for x = y, and I think it will always lie between the (old-version) values of x^y and y^x, at least for positive numbers.

[Anonymous No.1535664]

>>1535582
Oops, never mind, that won't work.

This thread is now about finding a real-valued function f(x, y) such that for all real x and y,
1. f(x, x) = x^x
2. f(x, y) lies between x^y and y^x

[Anonymous No.1535694]

>>1535664
<span class="math"> f(x,y) = \frac{1}{2}(x^y + y^x) [/spoiler]

[complete nerd No.1535733]

2+2=niggers.

hurr

[Anonymous No.1535749]

[Anonymous No.1535767]

deleting this thread, see
>>1535719

[Anonymous No.1535774]

TI-89
they rox