Infinity :: essays research papers

The mathematical notion of infinity can be conceptualized in many polar ways. First, as counting by hundreds for the rest of our lives, an endless quantity. It can also be thought of as digging a whole in hell for eternity, negative infinity. The concept I allow explore, however, is infinitely smaller 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 setting up matched correspondences between sets we see a few peculiarities. on that point are as many infixed deems as until now bite. We also see there are as many native numbers as multiples of 2. 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 compar able-bodied number of members as the set of natural numbers. The both have the same cardinality &6 1632o. 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 tack on one number to the set of evens, in this case 0 it appears that the fag set is larger, but when we shift the bottom set over our initial statement is true 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 said we can try to find larger sets of infinity. cantor was able to show that some infinite sets do have cardinality great than &61632o, given &616321. We must compare the irrational numbers to the real numbers to achieve this result. 1&616140.1426784352&616140.2937587783&616140.3839028924&616140.563856365&61614No matted which matching system we devise we will alw ays be able to come up with another irrational number that has not been proclivityed. We gather up only to choose a shape different than the first digit of our first number. Our second 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.