All Questions
2 questions
0
votes
2
answers
58
views
If $T=\lbrace -1,1 \rbrace$, show that $\mathbb{R}^{*}/\mathbb{R}^{+} \cong T$ is group under multiplication.
If $T=\lbrace -1,1 \rbrace$, with the Fundamental Theorem of Homomorphism group, show that $\mathbb{R}^{*}/\mathbb{R}^{+} \cong T$ is group under multiplication, where $\mathbb{R}^*$ is set of all ...
- 2,238
0
votes
0
answers
168
views
Proving that $(\mathbb{R},+) \cong (\mathbb{R}_{>1},\circ)$
Below I will give a proof of the title's question. I was not sure if I had to prove that each of the used bijections is a homomorphism as well, but I just wanted to also go through (perhaps trivial) ...
- 1,238