Universally true assertions
... Suppose x is a real variable. Then the statement “ ∀z(x + 3 ³ x) ” means that for every real number x, ...
... Suppose x is a real variable. Then the statement “ ∀z(x + 3 ³ x) ” means that for every real number x, ...
Designing Classes and Programs
... • But, it’s difficult to see how to use a direct proof in this case. We could try indirect proof also, but in this case, it is a little simpler to just use proof by contradiction (very similar to indirect). • So, what are we trying to show? Just that x+y is irrational. That is, ¬i,j: (x + y) = i/j. ...
... • But, it’s difficult to see how to use a direct proof in this case. We could try indirect proof also, but in this case, it is a little simpler to just use proof by contradiction (very similar to indirect). • So, what are we trying to show? Just that x+y is irrational. That is, ¬i,j: (x + y) = i/j. ...
Lecture 22 - Duke Computer Science
... You can run a Java program and never have any overflow, or out of memory errors ...
... You can run a Java program and never have any overflow, or out of memory errors ...
A Primer on Mathematical Proof
... is not enough to simply plug in a few numbers for x and check in those cases. Playing around with specific numbers may help you discover the proof, but it is not sufficient for the final proof write-up. In contrast, you can disprove a statement by finding a single example where the hypotheses hold b ...
... is not enough to simply plug in a few numbers for x and check in those cases. Playing around with specific numbers may help you discover the proof, but it is not sufficient for the final proof write-up. In contrast, you can disprove a statement by finding a single example where the hypotheses hold b ...
Monday, August 8: Samples of Proofs
... Let a b = a + b + 4. Then a k = a + k + 4 and if a + k + 4 = a, then k = -4. Consider k = 4. a 4 = a + 4 + 4 = a for all real values of a, and 4 a = 4 + a + 4 = a for all real numbers a. Hence if a b = a + b + 4 , then a 4 = 4 a = a for all a Reals. Proof by Induction: (Set up ...
... Let a b = a + b + 4. Then a k = a + k + 4 and if a + k + 4 = a, then k = -4. Consider k = 4. a 4 = a + 4 + 4 = a for all real values of a, and 4 a = 4 + a + 4 = a for all real numbers a. Hence if a b = a + b + 4 , then a 4 = 4 a = a for all a Reals. Proof by Induction: (Set up ...
lecture24 - Duke Computer Science
... You can run a Java program and never have any overflow, or out of memory errors ...
... You can run a Java program and never have any overflow, or out of memory errors ...
A(x)
... to the end of 19th century. At that time formalization methods had been developed and various paradoxes arose. All those paradoxes arose from the assumption on the existence of actual infinities. To avoid paradoxes, David Hilbert (a significant German mathematician) proclaimed the program of formali ...
... to the end of 19th century. At that time formalization methods had been developed and various paradoxes arose. All those paradoxes arose from the assumption on the existence of actual infinities. To avoid paradoxes, David Hilbert (a significant German mathematician) proclaimed the program of formali ...