Lecture 2 - inst.eecs.berkeley.edu
... say things that turn out to be false. A proof provides a means for guaranteeing such claims. Proofs in mathematics and computer science require a precisely stated proposition to be proved. But what exactly is a proof? How do you show that a proposition is true? Recall that there are certain proposit ...
... say things that turn out to be false. A proof provides a means for guaranteeing such claims. Proofs in mathematics and computer science require a precisely stated proposition to be proved. But what exactly is a proof? How do you show that a proposition is true? Recall that there are certain proposit ...
Introduction to Discrete Mathematics
... We will construct a number N so that N is not divisible by any pi. By our assumption, it means that N is not divisible by any prime number. On the other hand, we show that any number must be divided by some prime. It leads to a contradiction, and therefore the assumption must be false. So there must ...
... We will construct a number N so that N is not divisible by any pi. By our assumption, it means that N is not divisible by any prime number. On the other hand, we show that any number must be divided by some prime. It leads to a contradiction, and therefore the assumption must be false. So there must ...
XR3a
... Prove: The sum of an irrational number and a rational number is irrational. Proof: Let q be an irrational number and r be a rational number. Assume that their sum is rational, i.e., q+r=s where s is a rational number. Then q = s-r. But by our previous proof the sum of two rational numbers must be ra ...
... Prove: The sum of an irrational number and a rational number is irrational. Proof: Let q be an irrational number and r be a rational number. Assume that their sum is rational, i.e., q+r=s where s is a rational number. Then q = s-r. But by our previous proof the sum of two rational numbers must be ra ...
Writing Mathematical Proofs
... then use this assumption with definitions and previously proven results to show that the conclusion must be true. Direct Proof Walkthrough: Prove that if a is even, so is a2. Universally quantified implication: For all integers a, if a is even, then a2 is even. Claim: If a is even, so is a2. Pf: Let ...
... then use this assumption with definitions and previously proven results to show that the conclusion must be true. Direct Proof Walkthrough: Prove that if a is even, so is a2. Universally quantified implication: For all integers a, if a is even, then a2 is even. Claim: If a is even, so is a2. Pf: Let ...
