Infinity dabbling in Part III

Infinity dabbling in Part III Infinity is a floorless room without walls or ceiling. "- Anonymous For those who have followed my series of articles about the infinite, this article is the central question conceing the existence of different types of infinity. After reading the two previous articles, it is considered that the question of infinity is really strange. Over the centuries many philosophers and mathematicians have been debating this and more curious about its implications. From the fifth century Eleatics (greek philosopher of Elea: Zeno, Parmenides, and Melissus) all the famous German mathematician Georg Cantor, who is known as the father of the mode theory of the great thinkers who have thought and worked feverishly to try to nail a precise formulation this idea seems surreal. As explained in the previous quote, infinity challenge our notion of size that you can not put a dress around it, and yet based on the work of Cantor, the idea of a single type of infinity can be proved false. This concept is so mystifying and enervating the same time not believe that Cantor was his state of health in the face of constant complaint that he, by marrying the ideas of his contemporaries. What a price to pay for the march forward in the field of mathematics, such as Cantor's work has led to criticism in both functional analysis and database topology, the two branches at the top of this discipline. In any case, proof that the real figures are more numerous - shows that "more" infinite - that count the number is fairly simple. The implications of this test is the mind of acceleration and expansion of these tests, it provides a hierarchy of transfinite numbers. Before coming to the test (which is very simple and the difference of tests, I studied in college, which is absolutely necessary to develop and lots of coffee and a minimum of three aspirins to understand), I would like to make some preliminary observations and build on a couple of points regarding the actual number and what it means for them. The field of real numbers is all the account numbers (1, 2, 3 ,...}, negative account numbers {...- 3, -2, -1), all fractions (which we mathematicians call rational numbers - because they are of sound mind), and figures like the square root of 2, the square root of 3, the number pi greek, and 0. The question that we do here is that there are more decimal numbers range between 0 and 1, which is how the number 0.12, 0.0498, etc. of all the counting numbers (1, 2, 3, ...) . At first glance it would seem that since all the numbers, the count is infinite, infinity, and it means that there are no limits, no end, that n 'there is no limit - you get the picture - then should have the same number of elements between 0 and 1, as are account numbers. Ah, but there's the rub, this is not true for those of you who were thinking about the future, due in May have already tued up on you. Georg Cantor finally announced through his diagonal proof, but we will use an approach that is even easier. The method is also based on the concept of Cantor "connecting elements", which is known as a "one-to-one correspondence." (These two concepts were discussed in Part II of this article.) In fact, we are able to show how each element pair of accounting numbers with an element of the interval from 0 to 1. For example, you could pair 1 and 2 of 0.25 with 0.354. If you order to show that each account number is "tied" or related to a different number of 0 and 1, we have shown that all account numbers have been assigned a distinct group of numbers in this range. A When we did, then show that there are many numbers between 0 and 1 do not have "data", so to speak, there is the range of numbers in question. This means that there are many more problems in this series, and thus prove our thesis. Math is not great! So how can we do? Very simple. Now, watch carefully, because the simplicity of what is surprising. We have implemented the following one by one correspondence between the (1, 2, 3 ,...} and the interval from 0 to 1, as follows: 1 pair of us to 0, 1, 2 to 0.11 3 in 0111, and we always do. Now, each account number is linked to a single number in the range from 0 to 1. Of course, any number 0.1, 0.11, etc., was in the interval in question, and each one is different from another within the next year. For example, 0.1 and 0.11 differ by a penny, 0.11 and 0111 by a thousandth, and so on. Given that this trend is still in a way that each number in 0.1111111 ...... in the meantime, we have exhausted all the numbers count. Ah, but what is a number like 0.2 or 0046? The possibilities are endless. For each account number is already associated with a number of the interval from 0 to 1, these two new numbers are not represented in the head-to-face connection. Therefore, it takes a little 'more numbers in the range from 0 to 1, then all the account numbers and, therefore, we find that there is no doubt more than one type of infinity. Wow! When I leaed of this reality and its necessary extension, which leads the existence of an infinity of Infinities, so the my mind and I have lost a number of channels, as I had a headache for three days! Chew on that a little tidbit 'and see if you believe that the existence of God is so difficult to imagine.