A natural deduction proof goes from premmisses to conclusion, and under normal circumstances you will not assume the conclusion. Sometimes you may assume the negation of the conclusion and do some ...
There was a time when I avoided math proofs, but now I am starting to enjoy them. I am taking Intro to Linear Algebra and am falling in love with proofs. Are there any introduction to mathematical ...
I am reading Gödel-Escher-Bach and a good dialogue by Eliezer Yudkowsky and I think I might have understood the nature of the Completeness and Incompleteness theorems (at least regarding Peano ...
We know Euclid's axioms were found to be having many loopholes as in there were still many assumptions which weren't being stated in his system of axioms . Are Hilbert's axioms today completely ...
Sometimes there are multiple equivalent ways of defining the same structure; for example, topological spaces are determined by their open sets, but also by their closed sets. I'm looking for a way of ...
This is my follow-up question to my own query earlier: How can I algebraically prove that $2^n - 1$ is not always prime? Almost half of the answers said that I provided my own proof by giving ...
What do we mean when we say that a mathematical proof is elegant? Of course one can say that the proof is beautiful, but what do we precisely mean when we say that a proof is beautiful ? Is there a ...
The motivation for this question is : http://math.stackexchange.com/questions/4066/rationals-of-the-form-fracpq-where-p-q-are-primes-in-a-b and some other problems in Mathematics which looks as if ...