Methods of Proofs Recall we discussed the following methods of
... An implication is trivially true when its conclusion is always true. A declared mathematical proposition whose truth value is unknown is called a conjecture. One of the main functions of a mathematician (and a computer scientist) is to decide the truth value of their claims (or someone else’s claims ...
... An implication is trivially true when its conclusion is always true. A declared mathematical proposition whose truth value is unknown is called a conjecture. One of the main functions of a mathematician (and a computer scientist) is to decide the truth value of their claims (or someone else’s claims ...
An Example of Induction: Fibonacci Numbers
... Theorem 2. The Fibonacci number F5k is a multiple of 5, for all integers k ≥ 1. Proof. Proof by induction on k. Since this is a proof by induction, we start with the base case of k = 1. That means, in this case, we need to compute F5×1 = F5 . But, it is easy to compute that F5 = 5, which is a multi ...
... Theorem 2. The Fibonacci number F5k is a multiple of 5, for all integers k ≥ 1. Proof. Proof by induction on k. Since this is a proof by induction, we start with the base case of k = 1. That means, in this case, we need to compute F5×1 = F5 . But, it is easy to compute that F5 = 5, which is a multi ...
God, the Devil, and Gödel
... Descartes believed that (nonhuman) animals were essentially machines, but that humans were obviously not; for a machine could never use speech or other signs as we do when placing our thoughts on record for the benefit of others. … it never happens that (a beast) arranges its speech in various ways, ...
... Descartes believed that (nonhuman) animals were essentially machines, but that humans were obviously not; for a machine could never use speech or other signs as we do when placing our thoughts on record for the benefit of others. … it never happens that (a beast) arranges its speech in various ways, ...
The Logic of Conditionals
... you can be sure that there is an FT-proof of Q from P1,…,Pn, even if you have not actually found such a proof. ...
... you can be sure that there is an FT-proof of Q from P1,…,Pn, even if you have not actually found such a proof. ...
Lecture slides (full content)
... in term of final grade # 6%x50%=3% then it is below are the acceptable margin of error # 5% in physics then it is totally acceptable then it is not bad even if you left everything blank and others did well! ...
... in term of final grade # 6%x50%=3% then it is below are the acceptable margin of error # 5% in physics then it is totally acceptable then it is not bad even if you left everything blank and others did well! ...
