Recent content by supermiedos

Of course. I get it now. Thanks

Wait, so in this case we have like "two inductions" into one? We're assuming that m⋅n = n⋅m but also we're assuming that n⋅S(m) = n⋅m +n in the same proof?

But since S(n)*m = nm + m I'd like to prove that also m*S(n) = nm + m, thus S(n)*m = m*S(n), meaning that nm = mn

Homework Statement Let, m, n be natural numbers and S(n) the succesor of n. If S(n)*m = nm + m Prove that m*S(n) = nm + m Homework Equations The Attempt at a Solution

Thank you, both of you. I got it :)

Amazing! Thank you! I understood all steps, except one. How can I prove your last statement? Using symetry? And don't worry, it's not homework. I'm self studying mathematics :)

Thank you, I also tried it, but I got stuck

I tried it, but gotten nowhere

Hehe, don't worry. I was trying to use geometric arguments (showing that the area below sin^m(2x) equals the area belos cos^m(x), from 0 to pi/2). I can't see the way, also. Thank you for your help

Thank you for your response. As you said, the problem should have stated the "nature" of m. I tried first using your suggestion when m is odd. This is my procedure, but I got stuck: But I don't know what to do next.

Homework Statement I want to prove that: Homework EquationsThe Attempt at a Solution I tried using the trigonometric identity: sen2x = senx cosx / 2, so, I got: 1/2m∫(sen2x)mdx, x from 0 to pi/2, but now I don't know how to proceed. Can you help me please?

Thank you so much for your replies. I understand now :)

That's what confuses me. I tought since the problem states that we're going to find the unicity of the identity element of addition, we could use all the rest of the properties without questioning its unicity. Since 0' + 0* = 0´ and 0* + 0' = 0* then 0* = 0'. Is that correct?

That makes sense. So I must be explicit in the use of the properties. Thank you

Homework Statement Here, V is a vector space. a) Show that identity element of addition is unique. b) If v, w and 0 belong to V and v + w = 0, then w = -v Homework EquationsThe Attempt at a Solution a) If u, 0', 0* belong to V, then u + 0' = u u + 0* = u Adding the additive inverse on both...