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This is more of a semantic question than an actual math question but I couldn't see where better to put it.

If I would write a silly equation like the aforementioned $ \sqrt{"cat"} $, what is the proper name for the "cat" portion?

Can one say it's not in the domain? Is it a type error?

UPDATED

Perhaps I didn't explain it perfectly. Square Root, or Radical of "cat" makes no sense. I'm looking for the word that describes a data type that makes no sense in a mathematical context.

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So "cat" is a non-radicand? Not exactly what I'm looking for... I'll know the word when I see it –  Imray Jan 25 '13 at 19:08
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...and the anonymous down-voters are hovering again –  Imray Jan 25 '13 at 19:09
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@Imray, it is very difficult to make sense of your question, so it is not surprising that people are downvoting it. (And, as you probably know, there is absolutely no requirement for downvoters to leave anonymity, just us upvoters are not required to tell you their identity) –  Mariano Suárez-Alvarez Jan 25 '13 at 19:52
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The formal name of "cat" is Felis catus, see here: en.wikipedia.org/wiki/Cat –  dwarandae Jan 25 '13 at 22:15
    
@dwarandae lol! –  Imray Jan 30 '13 at 16:27

5 Answers 5

up vote 3 down vote accepted

+1 This is not a silly question, it a question that belongs to computer science or programming more than mathematics.

In mathematics one plays the role of compiler that is aware of the types that can be used, so there was no need to have a terminology for such instances.

However in programming, things like this are the bread and butter of programmers, specially in the strongly typed languages like Java,Delphi,C# etc. , but in languages like php one could very well get away with it until the expression needs to be evaluated (when program runs).

So borrowing from the cs/programming world words like : invalid argument (for the current context), unsupported argument (type) etc.

However if you have a way to define $cat^k$, then you can also formally define $\sqrt{cat}$ using formal Taylor power series.

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Thank you for understanding my question! I appreciate your answer. I suppose I'll settle for "invalid argument". –  Imray Jan 27 '13 at 17:15

This is a nice question. It, however, seems slightly philosophical.

If we look at $cat$ as being the multiplication of three variables $c,a,$ and $t$, then $\sqrt{cat}$ is defined in a mathematical context.

However, if we look at $c,a,$ and $t$ as letters which are not variables, $\sqrt{cat}$ has no mathematical meaning since $\sqrt{x}$ is a function from $\mathbb{R}$ to $\mathbb{R}$ or a relation from $\mathbb{R}$ to $\mathbb{C}$. In either case, $cat$ is not in $\mathbb{R}$. In fact, $cat$ does not even stand for a number.

I would think that the best way of expressing this is that $cat$ is "not in the domain".

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We say that the argument is "ill-typed" or "improperly typed" or something of that sort meaning that it is the wrong type of argument. The opposite is "well-typed".

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In the expression $\sqrt{x}$, $x$ is referred to as the radicand: http://mathworld.wolfram.com/Radicand.html

If you literally mean that you pass the string "$cat$" as an argument to the square root function (that is, if $f(x) = \sqrt{x}$ and you wish to compute $f(cat)$): It doesn't make sense to pass a string value to a numeric function. This is because strings are out of the domain of math... (essentially)

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Strings are out of the domain of math? Not really. (and I don't mean string theory) –  Rahul Jan 26 '13 at 2:48
    
That's why I wrote "(essentially)". ;) I guess I should have said "out of the domain of the square root function." –  anorton Jan 26 '13 at 2:53

The question is asking what we call the number whose root we are getting. Similarly, with the expression $\frac{dog}{cow}$, dog is the numerator and cow is the denominator.

In the case of $\sqrt{cat}$, cat is called the "radicand".

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No, this is not what the question asks. –  Mariano Suárez-Alvarez Jan 26 '13 at 2:32
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Then what is he asking? He stated that it is a question of semantics, i.e. the names of things. –  Richard Jan 26 '13 at 2:37

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