Question

- how and when it is possible or we need using the reductio ad absurdum prove-style ?- with examples please -

Answer 1

a classic example is to prove that
\[\sqrt{2}\] is irrational. this is because you are trying to prove it is NOT something.
obviously you do not have time to check every fraction, so you
ASSUME it is a fraction and then use "reductio ad absurdum" to show that you end up with something false.

this means your assumption was not true, i.e. in this case that
\[\sqrt{2} \] is NOT rational

Answer 2

ok ty. but for one equation like m=a+b for example - how us ? please

Answer 3

i am not sure what you mean
\[m=a+b\] is an equation, not a theorem. so you cannot "prove" it by any method

Answer 4

a theorem comes on the form of
" if something is true, then we know something else must also be true"

Answer 5

for example if we want to prove it that m is always even if a and b are odd

Answer 6

well that i think you can prove directly. i would not use it in this case. it is silly to use a proof by contradiction when you can prove something directly because it keeps you from explaining why exactly it works

Answer 7

this take three lines
1) if a and b are odd then
\[a=2j+1,b=2k+1\]
2)\[a+b=2k+1+2j+1=2(j+k+1)\] is even

Answer 8

ok two lines

Answer 9

ok and if m is even can be write always in the form 2n - so than if a+b=2(j+k+1)=2n than n=j+k+1 yes ?

Answer 10

"The opposite of every great idea is another great idea."

"This statement is false"