/sci/ - Science & Math

Mr. Conway would like to have a word with you.

It's correct, OP. Decimal representations of rational numbers aren't necessarily unique. Anyone who says otherwise is trolling or a retard. (I guess that's redundant.)

There *are* numbers smaller than any real number, however. If you call one of these numbers q, then you can say that r < 1-q < 1, where r is any real less than 1. However, that's not the same as saying there exists a nonzero q such that 1-q = 0.999.... Pic related.

I post this image in a thread just like this one every second day, yet there are still people who have not read it. Read this fucking book!

Posting reality in a troll thread.

>>2130744
Real mathematicians disagree.

No. # / 0 = undefined. # / epsilon = infinity, where epsilon is an infinitesimal (a number smaller than any real number but greater than 0).

If you're going to use infinities as numbers (which is ENTIRELY POSSIBLE), then you have to use infinitesimals too. 1/\infty = \epsilon

http://en.wikipedia.org/wiki/Surreal_number

Mathphysicsfag here. Would /sci/ be interested if I put together a little series of lessons on infinities, so that we are all better equipped to deal with this crap when it comes up, and also because they're really, really fun? Maybe an hour a night for a week or so? I could post a little discussion of some topic, and have some "homework" questions that /sci/ could work on together, and then people could ask me questions if they have any?

Also, just want to point out that the video in that link makes a fundamental error. At 1:28 it says, "the matter contained within the singularity must be infinite." What it means is that the density is infinite. But it neglects two facts. We don't know that there really was a singularity at the BB--we only claim to know information after 10^-43 seconds. And there is no physical law that says density can't be infinite anyway. And also, at t=0 if there was a singularity, space-time is one dimensional, so why would you even try to apply a four dimensional mathematical approach?

Just saying, it's not a very clever argument.

>>1783920
Read this and don't talk about infinity or use the word "number" again until you do.

Operation is not defined in a field.
/thread

>>1756228
^--- you: read this book, and don't ever talk about infinity again until you have.

It is correct, and make them read this book if they disagree.

Or, more simply, you can cite a Wikipedia entry with really shitty grammar and no good references (but which is still correct)
http://en.wikipedia.org/wiki/Decimal_representation
> Some authors forbid decimal representations with an infinite sequence of digits 9, which restriction still allows a decimal representation for each non-negative real number, and in fact makes such a representation unique.

<--- Everyone read this book and don't come back and argue about infinities and infinitesimals until you have. You make the rest of /sci/ look retarded. Yes, even that guy who asked about the scientific reason for having a taint looks slightly more retarded because of you.

They are all infinitely far from any infinity.

Infinity is totally a number. Well, it's a name that is given to many numbers, but it generally refers to the first number greater than any integer. It's not an integer, or a real number, but it's still a number.

I'm going to post this image every day from now on until /sci/ stops being mathematically illiterate.