Question

I feel like this doesnt need to be proved since you can just count them, but how do I show that x+x= 2x
and in general

Answer 1

in general, \[\sum_{i-1}^{n} x = nx\]

Answer 2

Using the distributive property.

Answer 3

Or factoring.\[x +x = 1x + 1x = (1 + 1)x = 2x\]

Answer 4

ah I like that, thanks. Very simple.

Answer 5

\[\underbrace{x + x + x + \cdots +x}_{n ~\rm times} = (\underbrace{1 + 1 +1\cdots 1}_{n~\rm times})x = nx\]

Answer 6

No problem :-)

Answer 7

What you want to prove is an axiom, and you might wanna use other axioms to prove an axiom (that might be harder).

Answer 8

Thats what I am doing I think, using properties of real vector space to show others hold. And it is quite tricky. But thank you for you help!

Answer 9

Heh :-P