An alternate set-theoretic representation of n-tuples

This is just a brief note regarding the alternate set-theoretic representations of -tuples. I had read in a text on set theory that the -tuple could be represented as a set in the form . I tried hard to think of other ways of representing such a tuple, but could not think of any then.

An exposition of some elementary inequalities

Short, clever proofs have played an immensely important role in the development of Mathematics. However, I can’t say I am a big fan of them. Mostly because I can never imagine myself coming up with those. Moreover, they don’t give a clear glimpse of the structure of what they prove. They just somehow manage to

I worry about “small” things. Let us take a ring . It is easy to prove that that . The standard proof works this way: . Adding on both sides, we get . This fact could be used to prove that . How? . Hence, as is the additive inverse of , and as every