# Which number set does log(0) belong to?

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1. Feb 28, 2016

### Garlic

Hello everyone,
Which number set does log(0) belong to? Or does it belong to any number sets?

2. Feb 28, 2016

### Samy_A

$\log(0)$ is not defined.
The most you can say is that $\displaystyle \lim_{x\rightarrow 0+} \log(x) = -\infty$.

You could say it belongs to the Extended Real Numbers, I guess.

Last edited: Feb 28, 2016
3. Feb 28, 2016

### HallsofIvy

Which then is part of the "extended real numbers".

4. Feb 28, 2016

### Garlic

Is this statement true: "Any number z is an element of the complex numbers set"
Are there any sets for numbers which aren't defined in the complex number set?
What happens when a theoretical mathematics researcher or a philosopher thinks outside the "normal numbers" box? Do they define an arbitrary set, or is there an outermost number set?

5. Feb 28, 2016

### Samy_A

One example:

https://en.wikipedia.org/wiki/Quaternion

6. Feb 28, 2016

### Garlic

7. Feb 28, 2016

### Samy_A

You certainly can define your set of "numbers" as you like (if a definition is useful, or maybe more important from a mathematical point of view, interesting, is another matter).
For example, numbers not related to the quaternions are the p-adic numbers.

8. Feb 28, 2016