Week 13
... Exercise 6: The fact “proved” to the left can be demonstrated just as well by drawing a line segment (with length 1) and dividing it over and over again in much the same way. Show this version of the proof without words. Exercise 7: Draw a new diagram like the one in the previous exercise, but this ...
... Exercise 6: The fact “proved” to the left can be demonstrated just as well by drawing a line segment (with length 1) and dividing it over and over again in much the same way. Show this version of the proof without words. Exercise 7: Draw a new diagram like the one in the previous exercise, but this ...
Week two notes
... Expressions with the same value, like 12 + 7 and 7 + 12, are equivalent expressions. You can use the Commutative and Associative Properties to write equivalent expressions. ...
... Expressions with the same value, like 12 + 7 and 7 + 12, are equivalent expressions. You can use the Commutative and Associative Properties to write equivalent expressions. ...
Math 248, Methods of Proof, Winter 2015
... 3. Prove (by contradiction) that there does not exists a smallest positive real number (that is there does not exists an r ∈ R such that r > 0 and, if s ∈ R and s > 0 then r ≤ s). Sometimes we will want to prove that a statement of the form (∀x)(P (x)) is false. If we do this by giving a constructiv ...
... 3. Prove (by contradiction) that there does not exists a smallest positive real number (that is there does not exists an r ∈ R such that r > 0 and, if s ∈ R and s > 0 then r ≤ s). Sometimes we will want to prove that a statement of the form (∀x)(P (x)) is false. If we do this by giving a constructiv ...
Introduction to Theoretical Computer Science, lesson 3
... Logical entailment in PL • He is at home (h) or he has gone to a pub (p) • If he is at home (h) then he is waiting for us (w) • If he is not waiting (w) for us then he has gone to the pub (p). h p, h w | w p • The table has 2n lines! Hence, an indirect proof is more effective: • Assume th ...
... Logical entailment in PL • He is at home (h) or he has gone to a pub (p) • If he is at home (h) then he is waiting for us (w) • If he is not waiting (w) for us then he has gone to the pub (p). h p, h w | w p • The table has 2n lines! Hence, an indirect proof is more effective: • Assume th ...
compactness slides
... The language of sentential logic, that is, the set of all wffs, corresponds to C ∗ , the intersection of all inductive sets w.r.t. B and F. By the unique readability theorem C ∗ is freely generated from the set of sentence symbols by the functions in F. This guarantees the uniqueness of the extensi ...
... The language of sentential logic, that is, the set of all wffs, corresponds to C ∗ , the intersection of all inductive sets w.r.t. B and F. By the unique readability theorem C ∗ is freely generated from the set of sentence symbols by the functions in F. This guarantees the uniqueness of the extensi ...
