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The atlas · 44 theses · 51 relationships
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3 theses in Logic & mathematics
A short proof by contradiction shows that assuming √2 is rational implies that a fraction in lowest terms has both numerator and denominator even. The result is proven within standard arithmetic.
Euclid's proof multiplies any finite list of primes and adds one. The resulting number is not divisible by any prime on the list, so some prime outside the list exists. The result is proven in standard arithmetic.
Validity concerns the form of an argument: if the premises were true, the conclusion would have to be true. It does not require that the premises actually are true. A valid form can be instantiated with false premises.
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