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I sometimes see numbers or constants or variables having exponents the operation signs, such as these:

$a^{+},~ a^{-},~ (1/4)^{+},~ k^{\pm},~ 0^{+},~ 0^{-}$

All I know is the zero to the power of plus and minus, which happens for me to know it from learning limits in calculus.

Can someone explain me what do they mean?

Thanks for the answers.

serkan
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    These aren't exponents, they are superscripts used to decorate the variables, in the same way as one can use subscripts to decorate variables. The meaning depends on the context. $a^+$ and $a^-$ are sometimes used in connection with limits $x \to a^+$ meaning that $x$ tends to $a$ from above. You need to give more context to get a definitive answer. – Rob Arthan Feb 14 '21 at 18:55

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Something superscripted as $+$ or $-$ means the following:

$a^+$ means that we are approaching $a$ from the positive side of $\text{x axis}$ or from the right side.

$a^-$ means that we are approaching it from the $-\text{x axis}$

Thus, $0^-$ means approaching $0$ from left and $0^+$ means approaching it from right side....

This is the same case with all the numbers.

Nandeesh Bhatrai
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  • You should say "with superscript", not "raised to the power". The superscript + doesn't represent an "operation" on $a$, it's just part of the notational construct $x\to a^+$, as Rob's comment explains. – Karl Feb 14 '21 at 19:29
  • Yes. I have edited it... But you get the point right? – Nandeesh Bhatrai Feb 14 '21 at 19:31
  • Your answer is right in one specific context. Without knowing the context of the OP's question, we can't be sure. E.g., if the context was ordered rings, $A^+$ would very likely mean the set of positive elements of $A$. – Rob Arthan Feb 15 '21 at 01:52
  • @Rob Arthan when the OP said that he happens to know "that" from calculus, the most suitable context became calculus. – Nandeesh Bhatrai Feb 15 '21 at 04:09