il blog di Biagio Raucci
There are many techniques to prove various statements. The simplest ones are direct proof, where you show that if the first statement (P) is true then the second statement (Q) is also true; the proof by contrapositive, where you assume that the negation of the second statement (~Q) is true and show that this forces…
Continua a leggere →Note that: After adding, Use the fact that (with replaced by and by ), we have Now, note that Now we use tre triangle inequality and the fact that :
Continua a leggere →The following proof was discovered by Tom M. Apostol, and was published as “Irrationality of the Square Root of Two – A Geometric Proof” in the American Mathematical Monthly, November 2000, pp. 841–842. In short, if were rational, we could construct an isosceles right triangle with integer sides. Given one such triangle, it is possible…
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