A short proof of the maximum conjecture in CR dimension one

A Short Proof of the Irreflexivity Conjecture

and proved that < is a linear ordering. Laver’s proof uses a large cardinal assumption that is not provable in ordinary mathematics. In a series of papers [ ], Dehornoy showed (without any additional assumption) that any distinct a, b ∈ A are comparable in < and reduced the word problem to the problem of existence of a distributive one-generated algebra A in which a < a does not hold for any a ...

A Short Proof of Kneser's Conjecture

In the paper a short proof is given for Kneser's conjecture. The proof is based on Borsuk's theorem and on a theorem of Gale. Recently, LOV~SZ has given a proof for Kneser's conjecture [4]. He used Borsuk's theorem. This fact gave the author the idea of the proof we present here. THEOREM (Kneser's conjecture [3]). If the n-tuples of a set of 2n + k elements are partitioned into k + 1 classes, t...

A Short Proof of Goldbach’s Conjecture

It was proved for every even number greater than or equal to 4, there is always a prime number which is the result of subtracting the even number with some prime. Therefore, it was demonstrated the strong Goldbach’s conjecture as a consequence of applying a modification to the sieve of Legendre.

A Short Proof of Moll's Minimal Conjecture

We give a short proof of Moll’s minimal conjecture, which has been confirmed by Chen and Xia.

A New Short Proof of Kneser's Conjecture

A Short Proof of Kohnert's Conjecture