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How do you pronounce $\mathbb{F}_2, \mathbb{F}_2^n, \mathbb{N}^k, [n] = \{1,\ldots,n\},$ and $S \subseteq [n]$ when you're reading a text?

I've just started reading more advanced math textbooks and these are appearing all the time.

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I think this is a matter of taste/preference. Personally, I read them as...

"eff-two," "eff-two-enn," "enn-kay," and "box enn."

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It's ultimately a matter of preference and taste. At some point in learning mathematics, it helps to "break away" the notation from spoken language to avoid distracting questions such as this. For instance, you know $\Bbb N$ refers to the natural numbers (and presumably know what those consist of): whether you call it "n", "the set of naturals", "the set of positive/nonnegative integers" (depending on convention), etc., you know what is being referred to, and that is what's important.

I've often heard both - an "abbreviated" name and the proper full name - interchangeably throughout my education. Personally, I think that the longer name makes the meaning behind the notation clearer if you're a novice, but this is purely a subjective thing. At the end of the day, as you get used to the notation, you'll immediately understand what a given symbol means rather than having to decipher it and all. How it's pronounced or said won't really affect that in the long run - what's important is what the notation conveys, rather than how it's said, at least where learning is concerned.

So as some examples, the shorter and longer names I've often heard for each notation you've brought up. But there's no "wrong" way to pronounce them inherently, so long as it's clear what is intended!

  • $\Bbb F_2$:

    • Short: "eff two"
    • Long: "the (finite) field of two elements"
  • $\Bbb F_2^n$: (similar for $\Bbb N^k$)

    • Short: "eff two to the n"
    • Long: "the n-ary product of eff two with itself"
  • $\Bbb N$:

    • Short: "n"
    • Long: "the naturals", "the natural numbers", "the nonnegative/positive integers" (depends on your convention whether $0 \in \Bbb N$ but that's another question altogether)
  • $[n]$:

    • Short: "bracketed n" (maybe? I don't think I've ever heard this said aloud)
    • Long: "the first $n$ integers" (you may specify "positive" as well, but I feel most people understand what this means)
  • $S \subseteq [n]$:

    • Short: "a subset of bracket n" (I guess? Not much shorter but whatever...)
    • Long: "S is a subset of the first n integers"
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