For unary functions f,g:X→Y, where X is any set and (Y,≤) is a poset, when you rephrase ∀ x∈X: f(x) ≤ g(x) in prose, do you write

  1. "f is bounded above by g" or
  2. "f is bounded from above by g" or
  3. "f is majorized by g"?



They say Math is the universal language -- it is beautiful in and of itself and only becomes ugly when you have to translate it into human speech.

To answer your question: I don't recall the meaning of all the symbols in that equation, but from what I do understand, I believe the most common way to say this is "f is bounded above by g".

However since this is language highly specific to Math, not every English speaker will know what you mean, and it's likely that these kind of phrases have a specific jargon that is most common. Also, Math is a field in which many are not native English speakers, so you'll probably hear a lot of variation.

As for "why" the answer is simply "convention". g(x) is a function that describes the upper bound on f(x), yes? Which is to say, f(x) can never exceed g(x). So from what I recall from my various math classes, "bounded above" is simply what they say to describe this relationship.

  • 1
    @LeonMeier you mean you said you, personally, are a "monotonously growing function"? That's actually hilariously clever. – Andrew Nov 15 '16 at 20:29
  • 1
    @LeonMeier it's actually fine, it's what is called self-deprecating humor. The ability to do this well is considered a positive trait. It says that while you may be boring, you're always improving. – Andrew Nov 15 '16 at 20:44

The normal usage in the US would be bounded from above rather than bounded above, which might be construed as being bounded from below. I have never heard of majorized. But the most common term in the US would be less than or equal to.

A standard translation of your symbols into spoken US English would be For any x in the set X, f of X is less than or equal to g of x.

You could confirm this with professional mathematicians by asking at non-commercial, free sites Math Help Forum or My Math Forum.

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