How is he this good at explaining hard concepts it honestly baffles me,my teachers explanations were so bad and hard to understand but Zeeshan explained it absolutely brilliantly.God bless you!
salam, no because when you are doing proof by contradiction you only need to find one case where the original statement doesnt work so doing 3k+1 only is fine
i did not understand example 3) we said that n must not be multiple of 3 however we wrote it as n=3k+1 , as we can factorise it to n=3(k)+1 and it is a multiple of 3 ?
3k+1 cant be a multiple of 3 as if you take a number (k) then x3 then add 1 it will never be a multiple of 3 as it is always 1 more than a multiple of 3
Uve proved that EVERY non multiple of three number squared will also not be a multiple of three, so theres no case where u can have a non multiple of three square to a multiple of three, so ur contradiction is wrong
@@jeffs_r_us7166 that's the point of the contradiction. It's supposed to highlight the fact that there's no case where you can have a non multiple of three square to a multiple of three, by stating that every non multiple of 3 will always ever square to a non multple of three
