# Math notation question

**URL:** <https://boards.straightdope.com/t/math-notation-question/256749>\
**Category:** Factual Questions\
**Created:** [July 25, 2004, 1:19am UTC](https://boards.straightdope.com/t/math-notation-question/256749 "2004-07-25T01:19:18Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![Larry\_Borgia](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/larry_borgia/32/156_2.png) [@Larry\_Borgia](https://boards.straightdope.com/u/Larry_Borgia)\
**Post date:** [July 25, 2004, 1:19am UTC](https://boards.straightdope.com/t/math-notation-question/256749/1 "2004-07-25T01:19:18Z")

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In a book I am reading on modern physics (reading it yes, _understanding_ it on the other hand… 😕🙂 ) I’ve come across the following passage

> [@](#):
>
> Each Radial factor…is equal to a polynomial…multiplied by an exponential factor of the form
> 
> ```
> exp{ -r/na[sub]0[/sub]}   
> 
> ```

My question is, what does the “exp” mean? does it mean the polynomial is raised to this power? Or does it mean the expression within the brackets is the base of an exponent? I haven’t ween this notation before.

later, in a discussion of half-life the book uses the following expression

```
x[sup]-n[/sup] =exp{-n lnx}

 from high school algebra I know that
                             ln x[sup]-n[/sup] = -n lnx

  But I'm having a bit of brain freeze on the exp{} notation.

                     Any help guys? Thanks in advance
```

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**Author:** ![Topologist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/topologist/32/3208_2.png) [@Topologist](https://boards.straightdope.com/u/Topologist)\
**Post date:** [July 25, 2004, 2:40am UTC](https://boards.straightdope.com/t/math-notation-question/256749/2 "2004-07-25T02:40:22Z")

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exp{x} is another notation for e[sup]x[/sup], where e is the base of the natural logarithm; “exp” is short for “exponential”. I’m not sure of the origin of this notation. It’s useful in computer programming but it’s also handy in mathematics, particularly when the exponent gets complicated. Now I’m curious which came first. Anyone?

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**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\
**Post date:** [July 25, 2004, 2:42am UTC](https://boards.straightdope.com/t/math-notation-question/256749/3 "2004-07-25T02:42:26Z")

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exp(x) means e[sup]x[/sup].

x[sup]-n[/sup]  
= (e[sup]lnx[/sup])[sup]-n[/sup]  
= e[sup] - n ln x[/sup]  
=exp{-n lnx}

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**Author:** ![Larry\_Borgia](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/larry_borgia/32/156_2.png) [@Larry\_Borgia](https://boards.straightdope.com/u/Larry_Borgia)\
**Post date:** [July 25, 2004, 2:48am UTC](https://boards.straightdope.com/t/math-notation-question/256749/4 "2004-07-25T02:48:29Z")

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Thanks! 🙂

I’ve just never seen this notation before.

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**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\
**Post date:** [July 25, 2004, 4:16am UTC](https://boards.straightdope.com/t/math-notation-question/256749/5 "2004-07-25T04:16:54Z")

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For what it’s worth, exp(x) = sum(x[sup]n[/sup]/n!, 0 \< n), and e is defined to be exp(1).

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**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\
**Post date:** [July 28, 2004, 2:18am UTC](https://boards.straightdope.com/t/math-notation-question/256749/6 "2004-07-28T02:18:36Z")

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> [@ultrafilter](#):
>
> For what it’s worth, exp(x) = sum(x[sup]n[/sup]/n!, 0 \< n), and e is defined to be exp(1).

Silly people, exp is the map from a real Lie algebra to its simply-connected real Lie group. In this case, the algebra in question is the unique one-dimensional real Lie algebra.

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**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\
**Post date:** [July 28, 2004, 2:22am UTC](https://boards.straightdope.com/t/math-notation-question/256749/7 "2004-07-28T02:22:31Z")

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> [@Topologist](#):
>
> exp{x} is another notation for e[sup]x[/sup], where e is the base of the natural logarithm; “exp” is short for “exponential”. I’m not sure of the origin of this notation. It’s useful in computer programming but it’s also handy in mathematics, particularly when the exponent gets complicated. Now I’m curious which came first. Anyone?

The e[sup]x[/sup] came first. It turns out to be very useful in all sorts of old calculations (compound interest, etc…). For various reasons, e was considered the “most natural” base, and given one exponential function all others can be calculated. using logarithms in that base.

Anyhow, as more and more complicated expressions started showing up in the exponent, e[sup]x[/sup] was dubbed _the_ exponential, and written as most functions are, so as not to unduly strain typesetters.