/sci/ - Science & Math

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that's not a good way of looking at it

the set of real numbers, as is any set, is defined axiomatically

>>7539417
>>7539418
Answer the question god dammit!

>>7539426
what if your question about the real numbers isn't answerable?

>>7539429
Last time I checked there isn't anything in math that is "unanswerable". Just give me a yes or a no.

>>7539431
>Last time I checked there isn't anything in math that is "unanswerable"
what resource did you check?

>>7539431
Check again.

>>7539431
no there are numbers beside the reals

>>7539413
>>7539431
The main problem is the following; how do you define the notion of a number existing? The reals exist axiomatically (a non-empty set).

>>7539436
Can you cut the shit and give me an answer?

>>7539413
no
if i make no money and borrow from people, i am worth negative dollars. take the sq rt of what i owe and u get an imaginary number. its just the sqrt of my net worth

>>7539413
Definitely.

>>7539440
you are refusing to accept my answer. i'm being patient actually.

>>7539450
Well, maybe I didn't like your answer.

>>7539455
that doesn't make it wrong.

>>7539457
Thank you for assistanting me, I don't appreciate your attitude though.

>>7539459
i'm glad that my responses felt as cool as the answer.

>>7539413

No, OP, there are other numbers, particularly complex numbers, but the number systems that we discover tend to be related to the reals, admittedly. The complexes certainly are.

The first goofy thing I'm noticing about this image is the incorrect visual intimation that there are "other" real numbers apart from rationals and irrationals (say, in that purple blob). Quite the opposite, the union of the rationals and the irrationals (these latter being EVERYTHING ELSE, that is, every other real number which simply is not a rational) is precisely the reals. If you wanted to account for, say, the transcendentals, it would be enough to represent them as a strict subset of the irrationals. There's no "purple-space" for those to wander off into; it doesn't exist, as long as we stay on the real line.

I've always liked the idea that we should just standardize a set of the naturals including zero, so that we have two unambiguous sets say W and N that everybody knows, and carry on with our various statements that either need or need not to have, zero. That said, the reference to "whole numbers" simply including zero does remind me of my high-school math education, where this idea was left to die.

I recall reading a Spark notes or similar one time which took the trouble to distinguish between strictly real numbers (having a complex part of zero) and strictly imaginary numbers, having a real part of zero. The statement was made, in this laminated abomination, that the reals and the imaginaries are /disjoint/. The stupid author had forgotten the origin. Fortunately, this item is not something I ever purchased.

I think I've even seen a diagram on wiki somewhere with some quibble-worthy gaffes, couldn't find it just now...

When you go beyond the NZQRC rubric into more granularity, these diagrams can be... tricky, I suppose!

>>7539475
lol thread hidden

>>7539477

This cheeky response of yours to my excellent, wonderful reply is wrong and unwarranted. Although now that I actually scroll up, OP does seem to be a teenager judging by his impatience.

>>7539413
No. A real number is any number not in existence.

>>7539431
First of all, that's untrue; there are plenty of unanswerable questions in maths.
Secondly, it depends on your definition of number. The reals are contained in the complex numbers, so most every mathematician would say there are numbers that are not real.

>>7539413
A real number is any element in this following set. And the elements in the set is a set itself.


Real number = { N, Z, Q, R }
Where N = {1,2,3....}
Z = {...-2,-1,0,1,2,3....}
Q = The set of numbers that can be
expressed as an quotient between two integers.

R in this case is generally the complement to the union between N,Z and Q. In English: Basically any number that is not a Natural-, integer- or a rational number.

R = ∁( N∪Z∪R )


Now to answer your question.
No number exist to most existentialist's definition of existence. However, according to my common sense I assume you are some sort of nominalist. Nominalism mathematics (kind of a philosophy of mathematics) tells us that numbers that 'exist' are those numbers that can be represented or exemplified in the real world.

For example, the number 2 can be exemplified in real life that actually exists by just showing 2 beans. The rational number 1/2 can be exemplified as a half pie slice and thus the rational numbers exist according to the nominalist.

When it comes to irrational numbers that are considered to be real numbers, we can't really examplify any of them as an nominalist. The pi can be represented as a circle however there are lots of irrational numbers a nominalist just has to deny its existence.


But a nominalist would agree, that a real number is any number that exist, given that numbers that exist are those numbers that can be represented and examplified using real existing things in Nature. However, they are denying a lot of irrational numbers that exist and thus some irrational numbers are not a subset of the real numbers according to the nominalist.

>>7539485
proof by contradiction is almost everywhere unhelpful. op was given sufficient information from any true statement made before you posted.

>>7539475
But i don't understand having this "whole numbers" shit. Never heard of it.
Isn't 0 included in the set of integers?

>>7539431

>>7539631

Actually, what seems really to have happened throughout the thread is that the OP, who we'll assume is a teenager due to >>7539426 and >>7539431 (where he may instead have shown his hand as a decent troll by veering off toward Gödel-land), instead decided to quickly derail his own thread with whining. The middle of the thread then became smug-posting about OP not being a cool kid who doesn't even incompleteness, while admittedly a few >>7539417 context-free >>7539438 replies were given, until I went into my thing (which admittedly began as a personal rant unto itself, but actually ended up having some context that the OP could have done something with had he cared to look).

Even the later-and-good post >>7539618 which also endeavors to be actually helpful, has the regrettable feature of using naive notation to describe "Real number".

So, contrary to what you've said, my above great post >>7539475 is actually both the first, and one of the must substantive things to have actually been written in an all-round very bitchy thread. Although yet again admittedly, one is not really moved in this place, to help the above ingrate which if you are the other poster that you sound like, does excuse your toying with him.

>>7539618
Would you mind converting the words in that image to FreedomSpeak?

>>7539637

Yes. 0 is an integer. Everything from ... -3, -2, -1, 0, 1, 2, 3 ... , and so on, is an integer, exactly as the OP picture suggests inside the "integer" segment. Notice that "Integers" there (also) includes the everyday positive counting numbers, 0, and the negatives of those everyday counting numbers.

Sometimes, depending on what part of math they're talking about, mathematicians may say that 0 is a natural number, or it isn't a natural number. Because sometimes you need to include or exclude zero to make whatever it is your doing, work. It actually doesn't matter though, because when they're doing things properly, the specify right at the top (of a proof, say) something like "when I say natural number, I mean 0,1,2,3..) or (1,2,3...). The reader's job is to check.

There is an old thing that I remember from high school classes where they specified "whole numbers" as being inclusive of zero. This distinction is not really bothered about in serious mathematics today (they just say what they mean, first), but I always had an affinity for it. Notice especially in the link, a few paragraphs down, that "there is no agreement... about whether to include zero."

https://en.wikipedia.org/wiki/Natural_number

The big feature of the natural numbers relative to the other systems is that there exists a smallest, or "least" element-it STOPS somewhere, at least, going in one direction. This will be either zero or one, depending on what you're doing.

The other, larger number systems (that we are concerned with, anyway) generally do not have this property-you can always pick something that's even more negative, i.e. less-than the first thing you picked. Not true with the naturals.

>>7539431
you arent asking a math question, you're asking a philosophical one you dingus

>>7539431
Is the answer to this question "no?"
srs question.

>>7539413
>Is a real number any number in existence?

The best short answer really is >>7539418
>that's not a good way of looking at it

The term "real" numbers can be misleading. Mathematicians think of real numbers as things that can be approached arbitrarily closely by an infinite sequence of *rational* numbers.

For example,

3.1, 3.14, 3.141, 3.1415, 3.14159, 3.141592, ...

is a sequence of rational numbers that approaches the real (and irrational) number pi.

Any point on the real number line can be approached in the same way. This is what distinguishes the real numbers. It's what is special about them.

There are other types of numbers that don't fit nicely anywhere on the number line, but mathematicians still use them and talk about them sensibly and rigorously. Since these other kinds of numbers are more abstract, they use axiomatic systems to reason about them very carefully. (Actually, they do this with the real numbers too.)

Those other types of numbers are still perfectly good numbers. They "exist," and are as "real" as the real numbers--in the philosophical sense.

>>7539953
Except there are real numbers where you can't compute their digits.
I.e. the number that are in the complement of the reals with respect to the set of computable numbers

en.wikipedia.org/wiki/Chaitin's_constant

https://en.wikipedia.org/wiki/Computable_number

>>7539413
This image confuses me. What real numbers exist that aren't rational or irrational.