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This is more of a notation question, but is there a (correct) way to use an operator as a variable? Like this perhaps$$\text{let H be} <$$ or $$H:<$$ Where $H$ is now equivalent to $<$

MarkW
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    Technically the concept of a variable operator is present in mathematical logic, abstract algebra, and computer programming. But in more commonplace, applied mathematics? Not so much. – C. Ventin Apr 05 '22 at 00:05
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    Often times equivalence relations are denoted by a letter such as $R$. You may write $aRb$ to say that $a$ is equivalent to $b$. – morrowmh Apr 05 '22 at 00:09

1 Answers1

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Nothing in mathematics says that letters represent "variables". All you are doing here is using a different symbol for the standard inequality symbol (which is not an "operator").

Redefining $<$ as $H$ would be legal but very confusing.

In some computer languages (lisp is one) you can specify operators as variables. For example, you might define a function this way:

f( a, b, op) 
   return a op b

Then

$f(3,4,+) = 7$ while $f(3,4,\times) = 12$.

Ethan Bolker
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