mathspp.com feed Stay up-to-date with the articles on mathematics and programming that get published to mathspp.com. 2021-09-15T23:55:57+02:00 Rodrigo Girão Serrão https://mathspp.com/blog/twitter-proofs Twitter proof: consecutive integers are coprime https://mathspp.com/blog/twitter-proofs/consecutive-integers-are-coprime 2021-09-15T23:55:57+02:00 2020-11-14T00:00:00+01:00

Let's prove that if $$k$$ is an integer, then $$\gcd(k, k+1) = 1$$. That is, any two consecutive integers are coprime. Do you have an idea for a twitter proof? Let me know in the comments below!

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Twitter proof: maximising the product with a fixed sum https://mathspp.com/blog/twitter-proofs/maximising-product-fixed-sum 2021-09-15T23:55:57+02:00 2020-11-05T00:00:00+01:00

Let's prove that if you want to maximise $$ab$$ with $$a + b$$ equal to a constant value $$k$$, then you want $$a = b = \frac{k}{2}$$. Do you have an idea for a twitter proof? Let me know in the comments below!

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Twitter proof: size of the set of subsets of a set https://mathspp.com/blog/twitter-proofs/subsets-of-a-set 2021-09-15T23:55:57+02:00 2020-08-06T00:00:00+02:00

Let's prove that, if a set has size $$n$$, then that same set has exactly $$2^n$$ subsets. Do you have an idea for a twitter proof? Let me know in the comments below!

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Let's prove that there are two irrational numbers, call them $$a$$ and $$b$$, such that $$a^b$$ is a rational number! And let's do it in a tweet. 