Naming variables

[factitious]

Imagine you're dealing with a formula which has a special type of variable in it. This variable is specified at the outset as being not equal to zero, which is good, because you need to divide by it as part of using the formula. However, the variable does get arbitrarily close to zero. In fact, you're pretty much taking the limit as it goes to zero. And at the end of this, when you get a result that involves this variable, you'll want to treat it as though it's equal to zero so that you can cancel out some terms. But despite this, the variable is by definition nonzero.

So the variable has an interesting and complex relationship with zero, and it's important not to add in any more confusion regarding this. Bearing all that in mind, what letter would you use to denote the variable?

If you said "the letter O," you have what it takes to be an 18th-century mathematician.

Comments

[erinmdmd.livejournal.com]

:-)

The geek in me misses math classes.

[ultraman.livejournal.com]

you think that's bad? you should read Hans Kamp's 1981 paper (A Theory of Truth and Semantic Representation) introducing discourse representation theory in which:

"u" and "U" are both used and have different meanings.
"m" and "M" are both used and have different meanings.
"v" is used, though I didn't see "V".
"k" and "K" are both used and have different meanings.
and the typesetting has the empty set symbol indistinguishable from greek letter phi, which sometimes occur in the same formula.

I should also note, he was in no way running short of other letters to use. There are whole chunks of the alphabet entirely unused by him.

oh, also, 's' and "S", again, both used, different meanings.

[factitiouslj.livejournal.com]

Uppercase and lowercase letters are fairly distinguishable. I have a commutative algebra book which uses blackletter/roman as a contrasting distinction.

[factitiouslj.livejournal.com]

Actually, having "a" be an element of a set called "A" is a commonplace in math.

[ultraman.livejournal.com]

'u' is not an element of 'U', though 'U' is a set, and 'u' is a member of some set.

also the version I have appears to be from a typewriter where the upper/lowercase distinction is harder to determine.

[merlinlocke.livejournal.com]

You rock my socks, boyo.

[factitiouslj.livejournal.com]

Thanks!

[thermoplyae.livejournal.com]

I found this journal because you seem to be the only other person on the planet interested in mathematical notation.

Keep it up! It is, in fact, plenty interesting.

In addition, i was used for infinity

[(Anonymous)]

That is something that would never be done by even the most ameature of modern mathemeticians.