MATHS proof by contradiction (1 Viewer)

[meomeo]

deary deary me D: I've forgotten how to do that already... can someone help.

I want to prove that root2 is irrational D: all I really remember is that it may (or may not) have had a p/q...

 

[Captain Gh3y]

Assume that sqrt(2) is the ratio of 2 integers p and q in lowest form, p/q = sqrt(2).
Then 2 = p²/q²
2q²=p²
Therefore p² is even; hence p must be even
Let p = 2m, m an integer
2q² = (2m)² = 4m²
q²=2m²
hence q is even
ie. p and q have a common factor, contradiction
Therefore sqrt(2) is irrational

b10

 

[sle3pe3bumz]

lol ? I dont think ive ever learnt something like this in my entire life .. LOL ! ><"

 

[ellen.louise]

probably, but still... holy shit that was smart!!! <i think that is buried somewhere in my masses of topic booklets courtesy of rego>:rofl:

 

[watatank]

Yeah assume a true statement is false, prove THAT statement to be the false so the opposite must be true.

 

[z600]

lol ? I dont think ive ever learnt something like this in my entire life .. LOL ! ><"

Its in the Cambridge Book.

 

[sle3pe3bumz]

Its in the Cambridge Book.

oh lol. shows what ive been doing with my textbook. ><"

 

[vulgarfraction]

it's like... a rigorous logical reducto ad absurdum, basically.