Infinity :: essays research papers

The numeric notion of timeless existence bathroom be conceptualized in many different ways. First, as counting by hundreds for the rest of our lives, an endless quantity. It can to a fault be thought of as digging a whole in hell for eternity, negative infinity. The concept I will explore, however, is infinitely little quantities, through radioactive decay Infinity is by definition an indefinitely large quantity. It is hard to grasp the magnitude of such an idea. When we examine infinity further by mintting up single-to-one equalizers between delineates we contain a few peculiarities. There are as many natural issuings as even numbers. We as well see there are as many natural numbers as multiples of two. This poses the problem of designating the cardinality of the natural numbers. The standard symbol for the cardinality of the natural numbers is &61632o. The set of even natural numbers has the same number of members as the set of natural numbers. The both have the same c ardinality &61632o. By transfinite arithmetic we can see this exemplified. 1 2 3 4 5 6 7 80 2 4 6 8 10 12 14 16 When we add one number to the set of evens, in this case 0 it appears that the bottom set is larger, tho when we shift the bottom set over our initial statement is lawful again.1 2 3 4 5 6 7 8 90 2 4 6 8 10 12 14 16We again have achieved a one-to-one correspondence with the top row, this proves that the cardinality of both is the same being &61632o. This correspondence leads to the conclusion that &61632o+1=&61632o. When we add two infinite sets together, we also get the sum of infinity &61632o+&61632o=&61632o. This being verbalize we can try to find larger sets of infinity. Cantor was able to cross-file that some infinite sets do have cardinality greater than &61632o, given &616321. We must(prenominal) compare the irrational numbers to the real numbers to achieve this result. 1&616140.1426784352&616140.2937587783&616140.3839028924&616140.563856365&61614No mater which matching carcass we devise we will perpetually be able to come up with another irrational number that has not been listed. We need only to take up a fig different than the first digit of our first number. Our entropy digit needs only to be different than the second digit of the second number, this can continue infinitely. Our new number will always differ than one already on the list by one digit.