Operators

knightstar · 2014-03-27 06:43:50

Defining an operator as an indicator of an operation raises some questions, such as in regards to exponentiation. Correct me if I'm mistaken, but I believe it can be said that...

addition is to the plus sign as
subtraction is to the minus sign as
multiplication is to the times sign as
division is to the over (or obelus) sign as

exponentiation is to the (?superscript?) sign as

nth root is to the radical sign as

logarithms are to the (?subscript?) sign?

Are the sizes of the exponent's and base's font in exponentiation and logaritms respectively, considered the indicator of the operation? Seems like a silly question, but if it's true it certainly is overlooked.
Also, why write LOG at all? Why not EXPO?

Last edited by knightstar (2014-03-27 07:04:43)

eigenguy · 2014-03-27 10:38:20

Please, subscripts are too useful as contravariant indices to be giving them another interpretation. To do so would just seed confusion (just as the combined use of superscripts to denote exponentiation, differentiation, repeated composition, and covariant indices can already be confusing). The traditional notation for logarithm works just fine.

Rather than considering LOG to be some sort of binary operator, we generally consider it to be a parameterized family of functions: ln is one function, log[sub]10[/sub] is another, log[sub]2[/sub] is a third, etc. From a strict logical standpoint this is the same thing as an operator, but it does tend to shape how we approach it, and how we denote it. Thus we want it to look like a function.

Font size has nothing to do with operation. We just prefer a smaller font for superscripts and subscripts in general for readability reasons. A full-sized font for them would either interfere with the surrounding lines are require more space between them.

knightstar · 2014-03-28 06:32:21

I don't completely understand, what is the visual indicator of the exponential operation if it is not font size?
When using a keyboard and the superscript option is not available, the caret (i.e. circumflex) is used. (e.g. 3^2=9)

Also, if I'm understanding the dual usage of LOG, then I believe this is true, correct?

[LOG] is to operator (of logarithms), and something else (i.e. a function) as
[-] is to operator (of subtractions), and something else (i.e. a negative number)

In other words, LOG is the operator of logarithms, and, when in doubt, the circumflex is used as the operator for exponentiation (otherwise the superscript is the visual indicator of the operation to be performed).
[it must be or we would have, e.g., 32 = 9, and obviously thirty-two does not equal nine]

I believe it's true to assume that all operations require an operator of some sort in order to indicate what operation is to be performed. Am I misunderstanding? In a manner of speaking, how do you know which way to go without a direction? I'm not trying to be difficult, I'm just looking for clarity.

Last edited by knightstar (2014-03-28 06:47:30)

eigenguy · 2014-03-28 09:34:37

Position, not font size, indicates exponentiation.

  10
10

still means 10[sup]10[/sup] despite the font sizes (this is the only way I've been able to show a superscript of the same size font - every other method appears to be disabled).

Use of Log as a function really isn't distinct from use of it as an operator, They are the same thing. It is a matter of how you look at it. Since you obviously have encountered functions yet, I wouldn't worry about it. You'll catch on later.

Circumflexes are a common way of denoting exponentiation in computer programs. The notation carries over into other fields. A variant some languages use is **, so 2^3 = 2**3 = 2[sup]3[/sup].

You can occasionally not have an explicit operator symbol. A common example, as you may be aware, is multiplication: 2x means 2 times the value of x, even though there is no operator symbol between them. As long as it is possible to differentiate between the two operands, juxtaposition (i.e, positioned next to each other) is a valid operation indicator.

(There is an even more common example. Another operator that we use all the time and denote by juxtaposition as well. But you may have a hard time recognizing it, because people don't normally think of it as an operation. I'll leave it to you to guess what it is.)

Math Is Fun Forum

#1 2014-03-27 06:43:50

Operators

#2 2014-03-27 10:38:20

Re: Operators

#3 2014-03-28 06:32:21

Re: Operators

#4 2014-03-28 09:34:37

Re: Operators

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