Using this type of math, we can get infinity minus infinity to equal any real number. Therefore, infinity subtracted from infinity is undefined. Now a limit is a number—a boundary. So when we say that the limit is infinity, we mean that there is no number that we can name. Therefore, infinity divided by infinity is NOT equal to one. Instead we can get any real number to equal to one when we assume infinity divided by infinity is equal to one, so infinity divided by infinity is undefined. If you divide zero by 2, you'll still get infinity.
Infinity divided by any finite number is infinity. Here are the rules: 1. Infinity divided by zero is not possible; 8. Zero multiplied or divided by anything is zero. Infinity divided in half is infinity. Infinity divided by anything is infinity so therefor anything with the word infinity equals infinity.
U can cut infinity,times infinity to the 5 power and wipe your It is the only thing that is unable to be changed. Infinity is not a defined number. It describes, in math, the endlessness of numbers. Instead we can get any real number to equal to one when we assume infinity divided by infinity is equal to one, so infinity divided by infinity is undefined. Infinite divided by infinite equals 1.
There's your answer. But infinity divided by infinity need not be 1. See for example, the paradox of Hibert's Hotel at the attached link. The answer remains infinity. There is no number greater than infinity. Infinity is defined to be greater than any number, so there can not be two numbers, both infinity, that are different. However, when dealing with limits, one can approach a non-infinite value for a function involving infinity. Take, for example, 2x divided by x, when x is infinity.
That value is indeterminate, because infinity divided by infinity is defined as indeterminate, and 2 times infinity is still infinity. But, if you look at the limit of 2x divided by x, as x approaches infinity, you do get a value, and that value is 2.
This does not mean that 2x when x is infinity is twice infinity, it just means that, right before x becomes infinity, the ratio is right before 2. Infinity should not be thought of as a number, but rather as a direction. Whereas a number represents a specific quantity, infinity does not define given quantity. If you started counting really fast for billions of years, you would never get to infinity.
There are, however, different "sizes of infinity. The infinity that describes the size of the real numbers is much larger than aleph-null, for between any two natural numbers, there are infinite real numbers. Anyway, to improve upon the answer above, it is not meaningful to say "when x is infinity," because, as explained above, no number can "be" infinity.
A number can approach infinity, that is to say, get larger and larger and larger, but it will never get there. Because infinity is not a number, there is no point in asking what number is more than infinity. Jerf mentions math education: I bet you could build a good number theory curriculum around that idea; giving number theory a REPL couldn't be all bad, given the abstraction of the topic. Patchwork defines subtraction: I guess I know now why infinity minus infinity is "indeterminate", rather than zero like I always thought it should be.
Jim Apple tackles the ordinals. Also, if you liked this article, you might want to check out The Haskell Road to Logic, Maths and Programming , which uses Haskell to teach discrete math. You can find a review in the Journal of Logic, Language and Information.
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Random code snippets, projects and musings about software from Eric Kidd, a developer and entrepreneur. You're welcome to contact me! Step 1: Counting First, we need to teach Haskell about the natural numbers. A number is either zero, or the successor of another number. Alan Manuel Gloria wrote on Feb 03, Mikael Johansson wrote on Feb 03, First off, your implementation of infinity is probably among the saner possible with a Peano arithmetic.
At least for the infinity Aleph I do, alas, not, however, know how this compares to the category CPO you're asking about; I would, however, suppose that it is a sane way to do it. Especially the one-point compactification of R or Jim Apple wrote on Feb 03,
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