When specifying the domain and range on a function, is it better to write it as:

when specifying the domain and range on a function, is it better to write it as:


D = -∞>y>∞
R = -∞>x>∞

or
x ∈ D : [-∞.∞]
y ∈ R : [-∞.∞]

or does it not matter?

Other urls found in this thread:

en.wikipedia.org/wiki/ISO_31-11
twitter.com/SFWRedditImages

Neither.

For the first one what you actually want is D = {x ∈ X : -∞>x>∞} or {x : -∞>x>∞}

For the second one, the symbol ":" usually means "such that", hence what you wrote makes no sense there.

What you want is x ∈ D = [-∞.∞]

For the range or you can just the notation for it, for some function f, f(D) is the range.
So f(D) = [-∞.∞]

You have your

my assumption was that it would be read as "x is in the element of the domain such that the domain is between positive and negative infinity"

Usually interval notation suffices.

what is X? the major problem is that this specified set is empty and i doubt that's what you wanted

isn't it wrong to use square brackets with infinity? i thought you needed parentheses so that it doesn't include.

>such that the domain is between positive and negative infinity
The domain is that interval, not just in it, hence the equal signs.

For the case where your domain is some interval I that is in between some other interval J, you can just say
x ∈ D = I ⊂ J

On the usual reals, yes, but on the extended reals for example you can do that just fine.

The preferred way among mathematicians is:

[math] D=x\in D: \{x\in D=\{x=x\in [-\infty, \infty]\}\}: -\infty

I just put it there since I assumed you're working with the reals, so you'd normally explicitly state that the domain is a subset of the reals (ie X would be some superset of your domain),

> R does not include ∞ or -∞
You are right.

>x∈(-∞,∞)
But then, I don't know if your ( ) are inclusive or not. If they are, then R U {-∞, + ∞} should be written.

The writing:
>x∈]-∞,∞[
seems more common. And those brackets are exclusive, so R can be used here.

You don't specify the range of a function, you describe it. You can only specify the domain and co-domain of a function..

>I don't know if your ( ) are inclusive or not
The interval [a,b] is inclusive and (a,b) is not. This is standard notation.
They're called "closed" and "open" intervals respectively, according to the topological notions

>() are standard notation
ok I knew it existed, but didn't know it had been standardized

> ] [ are standard as well
en.wikipedia.org/wiki/ISO_31-11

>everyone happy

Except only retards use ]a,b[ notation

() is more used but ][ is way more intuitive.

it's standard in France and it makes a lot more sense than ()

>][
O lawdy
I bet you the type of nigga that use f to denote an element of a general linear space

>using closing brackets as an opening bracket

They both semiotically succeed to connote the exact same thing. The "softness" of the parentheses versus the square braces connotes the nature of an open interval as opposed to a closed one, and of course reversed braces manage to do the same thing. Quibbling over notation is not a mathematically substantive point of discussion.

So since we're quibbling, my two bits: I've always found ]a,b[ to be a just-plain very ugly notation, for the simple reason that all brace-forms in every other context that I can think of, always face "in". Turning them out is aesthetically jarring to the point of being poor design, even if it is a perfectly logical conceit for their use (it is). Personally, I prefer (a,b). I am sure that it has happened many times over the years that brilliant European mathematicians have instead flubbed a [a,b] where they meant an ]a,b[. My suggestion being that the muscle memory to write (...), [...], even in other math contexts apart from the more general linguistic uses, is so overwhelmingly strong that this goof is liable to come up regularly, and never truly be mastered.

Also, the reverse brace notation to me smacks of goofy, nascent, yet-to-be-standardized type-setting, hard to read, the type of thing found in Principia Mathematica or a soft-bound Springer math book from the 60s and 70s, before TeX (pic related is a representative example).

But the above opinion is a purely subjective one based on my own geography and education (in Burgerland), just as the opposing opinion can make no claim to objective superiority. Since they each succeed to do the same thing. I've just suggested drawbacks to the European notation; a pushback on the American one is that the ordered pair notation (a,b) is liable to become confused by a neophyte with other contexts involving a like form (a point in the plane, etc) and that the reverse-brace notation eliminates ambiguity.

tl;dr one is really, truly not meaningfully better than the other, in this case.

>soft-bound Springer math book from the 60s and 70s
Made me chuckle senpai

In the context of babby-calculus, yes, this is correct. OP would better have asked,

"hey guise should I do

-∞ < x < ∞

or (-∞,∞)

(or equivalently in the latter case, to my above point, ]-∞,∞[ if you like that notation better.)

Personally I would encourage the OP to use the second of the three above forms when describing intervals which are subsets of the reals. In the case of closed intervals, you would then use closed braces a la [0,1]; Europeans and Americans agree on this aspect of notation.

In the case where a domain or an integral etc goes over "all the reals", or "the reals" (which amounts to the same thing) if your jargon is right you might write something like "the domain is R", "ranges over R in its entirety", "which has for its domain the reals", etc. Be very careful with this jargon though, especially if you're a noob. The above phrases all suggest that whatever it is you're doing applies over ALL the real numbers without exception, so if there /are/ exceptions (say, 0), then you need to declare them verbally, or othewise with your notation. Using interval notation to denote the reals is something that you do in Calc 1/high school calc to get comfy with the notion of interval notation itself, and then where you are discussing the reals themselves, it can often be replaced by the good old black-board bold R.

Also as someone else already said OP got his >

I live in the Netherlands and nobody I know uses ]a, b[

I appreciate your feedback!

After checking Wiki it appears that the introduction of the ]a,b[ notation is due to Bourbaki, which explains its traction in French mathematics. By dint of France alone I assume that it is used elsewhere in Europe, but that you've never seen it in NL is interesting to me.

>By convention, the lesser of the two endpoints is always written at left, followed by the greater one at right
OP did exactly that : he put -∞ on the left and ∞ on the right. But he misused the < >.

>OP wrote -∞>x
Reminder: the symbol > *must* have the lesser on the left and the greater on the right.
> instead of -∞OP wrote x>∞
The > symbol must have the lesser on the right and the greater on the left.
> instead of x

>the symbol > *must* have the lesser on the left and the greater on the right
I meant the symbol

Of course your first paragraph is right. You seem to have goofed in your second paragraph, however. The third paragraph is just a correct description.

Your usage of greentext throughout, funnily enough, does much to complicate the meaning and intent of your posts. It looks like you're just citing and being matter-of-fact, but even the hint of the possibility of sarcasm is enough to confuse. Funnily enough, even the "meme arrows" in their context add a further complication, and may even explain your goof in your second paragraph.

At the end of the above post, I had intended to indicate that in /interval/ notation, (as opposed to a chain of inequalities), the lesser element is always written at left. But I did not clarify this and you seem to have taken me to be referring to chains of inequalities (I wasn't but I failed to make that clear).

Thus you would always write something like

[-2,1]

or (-∞,80]

or ]-π, π[,

but never anything like ]2,-1[ or (5, -5) .

under normal circumstances. (although notations such as -5 < x < 5 and 5 > x > -5 are equivalent) The above (and forms like it) appears to be treated as a degenerate example which is equivalent to the empty set, but one would never write such a thing in normal practice. Intervals are most commonly used in practice as descriptors of "where the action is", although they are of course sets.

Of course, the latter paradoxical form is equivalent to

{ real x : 2 < x < -1 }

which is a compound requirement (this, AND this too) which no real number can satisfy. Thus the interval so described is empty, an absurdity.

Notice that this is quite different from, say, the union of two open intervals

(-∞,-1) U (2,∞)

Which are precisely the two disjoint open intervals to which any one above given real x is supposed to simultaneously belong. And of course, as we know, it just don't work.

that gave me a heart attack.

[math]The~Field~F~has~multiple~operations\\Some~x\inF: The~Function~\mathbb{T} (your curve)~produces~ "y_i \in y-axis=(\infty~or~"Some~arbitrary~end~point")"~values.\\ So T[x_i]=y_i\\\mathbb{X}=[-1,3] \quad but the graph seem to taper\\ From
~the ~field ~you~took~some~scalars, x_\emptyset,~x_1,~x_2,~...,~x_i\in\mathbb{X}\\
[/math]

[math]\text{Please use \text{}}[/math]

Just write it as f:D->R.