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Probably a silly question, but I could not find any reference.

How do you read $\mathbb{F}_2^n$ aloud?

This appeared when I tried to explain something to non-mathematics people (from other disciplines of science/engineering).

$n$-th order Cartesian product of finite field of characteristic $2$

This is what I said. Was it accurate?

I later explained in layman's term (i.e., the set of all $n$-bit Boolean vector) to them, not sure they understood.

soupless
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hola
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    "The set of all $n$-bit Boolean vectors" seems to be a decidedly non-layman description of this field. If your aim is the explain what this object is to a layman then I wouldn't even bother trying to succinctly pronounce it, because the only way you could do that is with technical terminology, which a layman will have little chance of understanding. Also isn't $\mathbb{F}_2$ the finite field of order $2$ rather than characteristic $2$? I know $\mathbb{F}_2$ has characteristic $2$ but it certainly isn't the only one. – SeraPhim Apr 27 '21 at 12:02
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    If you are talking to computer scientist/programmers, then they certainly know it as "all integers from $0$ to $2^n - 1$". Otherwise I would read it aloud as "N~DIMENSIONAL~VECTOR~SPACE~OVER~EFF~TWO~~~". – WhatsUp Apr 27 '21 at 12:05
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    I would say "eff two [pause] to the en", though probably saying the vector space et cetera is the right way. (by the way, I wonder if "eff to the en of two" is a thing...) –  Apr 27 '21 at 12:10
  • I would say $K^n$, so "$K$ to the $n$" with $K=\Bbb F_2$. – Dietrich Burde Apr 27 '21 at 12:23
  • Generally, I say "eff two to the n" (pretty literally) – tbrugere Apr 27 '21 at 12:28
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    I would be careful about making the distinction between $\Bbb{F}2^n$ and $\Bbb{F}{2^n}$. Not a native user of English, but I would probably call these "eff-two-en" and "eff-two-to-en" respectively. I would read $\Bbb{R}^n$ simply "arr-en", and when we discuss the vector space rather than the extension field, it feels logical simply to replace $\Bbb{R}$ with $\Bbb{F}_2$. – Jyrki Lahtonen Apr 27 '21 at 12:50

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As with most terms in mathematics, I read it the first time with a gloss:

"(while writing $\Bbb F_2^n$) "This denotes all lists of exactly $n$ zeroes and ones, which I'll call eff-too-enn from now on..."

Depending on your intended use of that set, I might follow up with "such a list constitutes a binary representation of a number between $0$ and $2^n - 1$", or "that is to say, points in the $n$-dimensional vector space over the field with two elements."

Subsequent times I just say "eff-too-enn".

John Hughes
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