Proof: direct, cases, contradiction and induction
Prove that odd + odd is even with algebra, check a claim by splitting it into cases, prove that there is no largest even number by contradiction and take the induction step for the odd numbers.
- سوريا: الصف ١٢
- فلسطين: الصف ١١
- إيران: الصف ١٠
- أفغانستان: الصف ١٠
- أوكرانيا: الصف ٧
- روسيا: الصف ٧
- فرنسا: الصف ٧
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
An example is not a proof. A proof must work for every case. In a direct proof you write the numbers with letters, for example an even number is ٢k and an odd number is ٢k + ١, and follow the algebra.
Proof by exhaustion splits the claim into a few cases that cover everything (even or odd). Proof by contradiction assumes the opposite of the claim and shows that it leads to something impossible.
Proof by induction has two steps: show that the claim is true for the first number, then show that if it is true for k, it is true for k + 1. Together they are like dominoes: the first falls, and each one knocks down the next.