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12 cards from this deck
Assume the opposite of what we want to prove is true
Do math until a contradiction arises
Conclude the original statement must be true
Not all numbers are even
There exists at least one A that is not B
ab\frac{a}{b}ba where aaa and bbb are integers with no common factors
There exists a greatest integer kkk
k+1>kk + 1 > kk+1>k contradicts kkk being greatest
There exists odd n2n^2n2 such that nnn is even
2k+12k + 12k+1
2=ab\sqrt{2} = \frac{a}{b}2=ba, no common factors
aaa and bbb both even, share common factor of 222
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