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sign

The word sign is used to refer to the symbols “ +” (the plus sign) and “ ” (the minus sign). The word is also used to refer to the question of whether an expression represents a real number that is positive or negative.
Example

If , you may say

“For negative x, f(x) and f'(x) are opposite in sign.”

Observe that for negative x, the expression f'(x) denotes a negative number even though the expression has no negative sign in it.

The word sign is also sometimes used to refer to other symbols, for example “the integral sign”.

subscript

An expression such as commonly means that a is the entry indexed by 2 in a sequence. Since a sequence is a function on its index set, authors may refer to as a “function on I”, and use language such as “a is increasing in I”.

subtract

Removing objects from a collection

In ordinary English, if you subtract from a collection you make it smaller, and if you add to a collection you make it bigger.

Applying the operation of subtraction

In math, “adding” may also refer to applying the operation of addition; but then a + b is smaller than a if b is negative. Similarly “subtracting” may refer to applying the operation of subtraction; but then a b is bigger than a if b is negative.

Both these usages (adding to a collection and applying the operation of addition) occur in mathematical writing. See minus.

such that

For an assertion P, a phrase of the form “ c such that P(c)” means that P(c) holds.

Examples

¨ “Let n be an integer such that .” means that in the following assertions that refer to n, one can assume that .

¨ “The set of integers n such that “ refers to the set . (See setbuilder notation. and the.)

Remarks

¨ Note that in pronouncing the phrase “such that” is usually inserted. This is not done for the universal quantifier. So “x(x>0)” is pronounced “There is an x such that x is greater than 0”, but “ x(x>0)” is pronounced “For all x, x is greater than 0”.

¨ Yes, I know that “ x(x>0)” is false.

sufficient

P is sufficient for Q if the statement “If P, then Q” is true. You can also say P suffices for Q. The idea behind the word is that to know that Q is true it is enough to know that P is true. See conditional assertion.

superscript

An expression such as may denote a to the nth power, but it may also indicate that it is the nth entry in a sequence indexed by superscript i. Typically superscript indices (see plural) occur in conjunction with subscript indices, but it is perfectly possible and common in some fields for superscript indices to occur without subscripted ones.

symbol

The word symbol, as used in math, is a typographical character or expression that stands for something. I am too intimidated by the entries in Mathworld and Wikipedia to try to write a more detailed explanation of the idea.

Symbols used in math include characters such as x, , and . Symbols in math may also be compound; for example the Legendre Symbol has the form (a/p), where a is an integer and p is a prime number.

symbol manipulation

Symbol manipulation is the use of algebraic rules, or rules of some other computational system, to change a symbolic expression to an equivalent one. For example, you can change to the equivalent expression using the distributive law for algebra, and you can change into using an integration rule.