Using proof by contradiction vs proof of the contrapositive
203 What is the difference between a "proof by contradiction" and "proving the contrapositive"? Intuitive, it feels like doing the exact same thing. And when I compare an exercise, one person proves by …
Are the "proofs by contradiction" weaker than other proofs?
Do logicians think that proofs by contradiction are somewhat weaker than direct proofs? Is there any reason that one would still continue looking for a direct proof of some theorem, although a proof by …
proof writing - Are There Any Symbols for Contradictions?
Is there any international icon or symbol for showing Contradiction or reaching a contradiction in Mathematical contexts? The same story can be seen for showing that someone reached to the end …
logic - Using proof by contradiction and a counter example ...
Jul 13, 2017 · A proof by contradiction is a proof of a statement by assuming there is a counterexample and then deriving a contradiction from that supposed counterexample , a classical case being the …
Understanding Euclid's proof that the number of primes is infinite.
Apr 7, 2016 · Here we have the usual historical mistake, dating back at least to Dirichelt, which holds that Euclid's proof was by contradiction. Euclid's actual proof was simpler and better than that.
Prove that the square root of 3 is irrational [duplicate]
The number $\sqrt {3}$ is irrational ,it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us Assume that it is rational and then prove it isn't (Contradiction). So the …
Proof of infinitely many prime numbers [duplicate]
In proof by contradiction you prove proposition A by assuming A is not true, and through a series of logical steps reach an impossibility, thus proving that A must be true.
logic - Can every proof by contradiction also be shown without ...
388 Are there some proofs that can only be shown by contradiction or can everything that can be shown by contradiction also be shown without contradiction? What are the advantages/disadvantages of …
elementary number theory - Proof of infinitely many primes ...
For some people, proof by contradiction is a capital sin, hence they rush to defend the honor of a long dead mathematician. What I don't like about the proof as it was presented to you is that it has the …
How can you prove that the square root of two is irrational?
Mar 14, 2016 · The descent method in the standard proof is, of course, hidden in the prime factorization proof, but that's a fine place for it. Note that the original poster couldn't grasp the popular proof, and I …