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

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

anonymous · Answer

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

parthkohli · Answer

Using the distributive property.

parthkohli · Answer

Or factoring.$$x +x = 1x + 1x = (1 + 1)x = 2x$$

anonymous · Answer

ah I like that, thanks. Very simple.

parthkohli · Answer

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

parthkohli · Answer

No problem :-)

parthkohli · Answer

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

anonymous · Answer

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!

parthkohli · Answer

Heh :-P