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Suppose I have three real scalars $a$, $b$ and $c$. I know $a>b$ and $a>c$, but know nothing about the relationship between $b$ and $c$. Like this question I want to express this relationship mathematically in a sentence, but I want to do so without using functions or writing it out in words.

Question

Is there a "proper" and unambiguous mathematical expression to express this? (Bonus: If so, what is it?)

Guesses

My first guess was:

$$a>b,c$$

but I realized it could be interpreted as $a>b$ with a hanging $c$. Then I thought this might work:

$$a>(b,c)$$

but then I wondered if it would look like $(b,c)$ was an ordered pair or something. I thought we might be able to borrow from set theory, but this question indicates not.

The suggestions from the answer to this question are either

$$ a \text{ is greater than either } b \text{ or } c\text{,}$$

which is rather wordy, or

$$ a > \max(b,c) \text{,}$$

which resorts to using a function. I expect that there is a way to express this notationally. My question differs from this question in that while I would like to know the notation (that answer belongs to that question), I'm asking whether such a notation even exists.

jvriesem
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    $a >b,c$ is clear, although $a > \max(b,c)$ is even clearer. I agree with Lord Shark's comment (below), but as an altenative, you could write $a >b,;a > c$. (since in this context, the comma means "and"). – quasi Feb 08 '18 at 19:28
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    What's wrong with "$a>b$ and $a>c$"? Is avoiding words really a good thing? But if you do want to avoid words, and make it a bit harder to read, how about $(a>b)\wedge(a>c)$? – Angina Seng Feb 08 '18 at 19:29
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    It's very common to use the comma on the LHS. Examples: $(1);x,y,z > 0$;$;(2);u,v \in S$. So if you don't like $a > b,c$ (although I see nothing unclear about it), you could instead write $b,c < a$. – quasi Feb 08 '18 at 19:46
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    You could write $bc$. – Deusovi Feb 09 '18 at 07:57

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