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I am trying to study lineair algebra on my self, and I came across a weird phenomenom "abusing a notation" What do they mean by that , does that mean that it isnt mathematical correct? Or is it a connection that doesn't really have meaning?

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  • $\begingroup$ Hard to say, unless you specifically provide background. For example, what is the exact wording of the source document's definition of a function? $\endgroup$
    – user2661923
    Jul 3, 2021 at 12:13
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    $\begingroup$ Your last three questions all contained pictures of text. I want to urge you to replace them by actual text with formulas typeset using MathJax. The reason is that pictures of text are not searchable, they are not accessible to those using screen readers, and they don't show up in question summaries. Please have a look at How to ask a good question. $\endgroup$
    – Christoph
    Jul 3, 2021 at 12:30
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    $\begingroup$ See the Wikipedia article on Abuse of notation. $\endgroup$
    – Joe
    Jul 3, 2021 at 12:54
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    $\begingroup$ @OogwaysStaf: Wikipedia is mostly accurate on mathematical topics. It gets a bad rap for no reason. By the way, if you want to notify me when you comment then you should begin your comment with @Joe. $\endgroup$
    – Joe
    Jul 3, 2021 at 13:20
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    $\begingroup$ @OogwaysStaf You're expected to put in some effort in writing and formatting your questions when you expect others to put in the effort to provide help and answers. $\endgroup$
    – Christoph
    Jul 3, 2021 at 14:15

2 Answers 2

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Strictly speaking, if $f(z) = z^k$, then the function is $f$, not $z^k$. But going through the contortions to add another layer of notation would only obscure the plain meaning. So since "we all know" that by $z^k$, we mean the function $z \mapsto z^k$, then let's just write $z^k$.

This depends on what definition for "function" your text actually uses, so I'm guessing a little bit here.

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It means I think that it is not technically accurate to describe $z^k$ as a "function", as it is really a polynomial, i.e a formal expression involving powers of $k$. There is a technical distinction to be made between a polynomial and the corresponding function, but they often can be regarded as the same thing. I am not sure how clear my explanation is to you, but basically the comment in the text can be ignored.

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