Is there any math notation for be denoted by?

https://mathoverflow.net/questions/325185/is-there-any-math-notation-for-be-denoted-by

The sentence s "In many supervised learning problems one has an output variable $$y$$ and a vector of input variables $$x$$ described via a joint probability distribution $$P(x,y)$$" from wiki

Here s implicitly declares 3 notations $$\{x,y,P(x,y)\}$$.

So I wonder if there is a math notation appeared in any famous book so that I can explicitly declare some notation in handwriting notes and plaintext digital notes

For example, if we can use @, then s equals to "In many supervised learning problems one has an output variable @ $$y$$ and a vector of input variables @ $$x$$ described via a joint probability distribution @ $$P(x,y)$$", in my personal notebook it's very handy and clear.

And I think notation := cannot be used in sentence s.

• If $:=$ cannot be used in a sentence I don't see why $@$ can be. Ordinary English sentences are fine. – Jair Taylor Mar 12 at 4:17
• @JairTaylor @ is just a notation example, if you use := , sentence will be unnatural – Voyager Mar 12 at 4:19
• You as an author are free to use whatever notation you consider "natural". It is not clear from the present formulation what you are trying to do... a notation for "is denoted by" strikes me as rather circular. But if you expect others to read what you write, you should define your notation whenever it is potentially confusing. If only you will read your handwritten notes, then such internal documentation will serve only to help you recall what you were trying to say. – hardmath Mar 12 at 4:23
• @hardmath , can you imagine how to use := in sentence s? It's not my subjective feeling. I just want to know if any famous book has such notation. – Voyager Mar 12 at 4:30
• Generally I do not see $:=$ used in a sentence in a text, unless both the left and right sides are symbols, and rarely then. It may be used informally on the chalkboard, etc. – Jair Taylor Mar 12 at 4:38