0

What is the best way to learn the meaning of the math symbols beyond the alphabet or the cardinal numbers?

I understand some

ϵ>0 means epsilon is greater than zero

∃δ>0 means there exists delta greater than zero

How should I say these?

∀x,y∈R, δf∘g=min{δ,δ1}, and f∘g

Ghid
  • 39
  • 2
    Without some context, "∀x,y∈R, δf∘g=min{δ,δ1}, and f∘g" doesn't make sense – Simon S Jan 29 '15 at 00:09
  • Thank you for your help, but I don't understand why context is necessary. The letter A, and the number 9 have meaning. Surely the symbols, ∀, ∈, and the little circle between the letters f and g, line in f∘g must have meaning in any context. – Ghid Jan 29 '15 at 00:16
  • 2
    $\forall$ is read as "for all". $\in$ is read as "in" or "is an element of". $f \circ g$ is read as "$f$ composed with $g$." But those are just words. Words without meaning aren't worth a lot. Meaning comes from context. In any case, your mathematical sentence doesn't really make a whole lot of sense, so it's hard to translate, other than literally, what's going on. It's like translating a colloquial phrase from a different language literally. – Emily Jan 29 '15 at 00:18
  • 1
    To expand on @Arkamis comment, it is certainly true for instance that it's well known what the composition of functions $f \circ g$ means. But the part "and f.g..." looks like a sentence chopped off. – Simon S Jan 29 '15 at 00:27
  • 2
    Actually the letter A doesn't have meaning in mathematics. It's free for being given a meaning, temporarily, whenever we have a meaning that we need to be carried by some letter, but by itself it has none. – hmakholm left over Monica Jan 29 '15 at 00:44
  • Is it actually three different expressions you are asking about? – Henrik supports the community Jan 29 '15 at 10:00

3 Answers3

2

Symbols carry meaning contextually. Sure, they have a literal "English" counterpart, but the sentence "plums deify" is pretty much nonsense, unless you're readying a fictional work in which plums are intelligent and have organized some kind of religion. In order to separate these kinds of nonsense sentences from the ones that really do make sense, you have to learn the context.

So to that end, I think your best bet is to figure out where those symbols you are looking at are coming from, and study some of that material. If I had to take a guess as to what you would be looking at when you encountered something like that, I'd venture to say it's some kind of elementary analysis text. So maybe try out a book like Ross's Elementary Analysis. It is very beginner friendly, and will teach you all the necessary notation used in the foundations of analysis.

A. Thomas Yerger
  • 17,862
  • 4
  • 42
  • 85
0

Here is where I used to go to learn new symbols.

Also, if $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ are functions, we write $g \circ f$ for the unique function $X \rightarrow Z$ specified by the following constraint.

$$\forall x \in X : (g \circ f)(x) = g(f(x))$$

This is called composition of functions. Make sure you also learn the terms "domain" and "codomain".

Also, notice that the notation for composition of functions is kind of backwards. Therefore, I write my arrows backwards to compensate: as in, if $g : Z \leftarrow Y$ and $f : Y \leftarrow X$, then $g \circ f : Z \leftarrow X$.

goblin GONE
  • 67,744
-1

Juast read and learn math and you'll see that there is nothing to learn ;)

pw1822
  • 698