I just would like to ask for the proof of this Corollary: |a| divides |G|.
In a finite group, the order of each element of the group divides the order of the group.
(The theorem is Lagrange's Theorem: |H| divides |G|.
If G is a finite group and H is a subgroup of G, then |H| divides |G|...
Hi guys, I'm doing a case by case proof of
|a+b| \leq |a|+|b|
from Spivak, and he says:
When a \geq 0 and b \leq 0, we must prove that:
|a+b| \leq a-b
I'm a bit stuck on his line of reasoning, could someone explain why we have to prove the above?
Can someone do this question please ? I can't do it.
Prove that if |A| ≤ |B| and |B| ≤ |C| then |A| ≤ |C|
Note: |A| ≤ |B| means "there exist an injection from set A into set B" and so on for the rest.
I would really appreciate it if someone can help me because I find this...