Tags » Finite

Zero and Infinity

To see the world in a grain of sand, and to see heaven in a wild flower, hold infinity in the palm of your hands, and eternity in an hour. 145 more words

William Blake (1757 - 1827)

To see a world in a Grain of Sand,
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand,
And eternity in an hour. 70 more words

Sum-Product Type Estimate for when A is a subset of R

As mentioned in earlier posts, many researchers have tried to extend Erdős and Szemerédi’s idea to different fields and rings. A natural extension to consider would be taking to be a subset of the field of real numbers, . 948 more words

Combinatorics

Every finite integral domain is a field.

Theorem.
Every finite integral domain is a field.

Proof.
Let R be an integral domain. So, is a commutative ring with an identity . Now, the only thing left to prove is to show that… 21 more words

Algebra (Hungerford)

The Paper That Started It All - Finding a Bound on Sums and Products of Integers

As mentioned last time, the paper by Erdős and Szemerédi sparked interest in many mathematicians’ hearts. As such there have been many papers written which extends Erdős’ and Szemerédi’s idea into other rings and fields; the field of real numbers, the field of complex numbers, finite fields of prime order, and lastly rational functions over a finite field of prime order. 1,268 more words

Combinatorics

The Big Crunch

In physical cosmology, the Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space… 439 more words

Universal

Sum - Product Type Estimates for Finite Sets of Various Rings and Fields - An Introduction

This is going to be a short post, but I wanted to introduce all of you into a literature review that I am currently working on. 319 more words

Combinatorics