(adsbygoogle = window.adsbygoogle || []).push({}); Hello, I’m Charlie and I’ve been trying to understand how I prove things correctly. So here is an example of the way I demonstrate:

Proof that square root of 2 isn’t rational

Consider the following hypotheses

1.(√2 is rational) → (√2 = m/n | m,n ∈ ℤ, gdc(m,n) = 1) → (m² = 2n², n = (m²)/2 | m,n ∈ ℤ, gdc(m,n) = 1)

2.(∀x,y ∈ ℤ, (x² = 2y²) → (x = 2z | z ∈ ℤ))

3.(m = 2k, n = 2p | m,n,k,p ∈ ℤ, gdc(m,n) = 1) → (gcd(m,n) = 1 ∧ gdc(m,n) ≠ 1)

4.~(gcd(m,n) = 1 ∧ gdc(m,n) ≠ 1)

By 1 and 2 there is

5.(√2 is rational) → (m = 2k, n² = 2k² | m,n,k ∈ ℤ, gdc(m,n) = 1)

By 5 and 2 there is

6.(√2 is rational) → (m = 2k, n = 2p | m,n,k,p ∈ ℤ, gdc(m,n) = 1)

By 6 and 3 there is

7.(√2 is rational) → (gcd(m,n) = 1 ∧ gdc(m,n) ≠ 1)

By 7 and 4 there is

8. ~(√2 is rational)

∎

Is it correct? If not, why? Any other observations?

Note: English is not my first language, and I’m not really good in it. So, I apologize for any mistakes.

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# How do i demonstrate?

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