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This is also known as a falling factorial or backward factorial, and the () notation is a Pochhammer symbol. [96] Falling factorials count the number of different sequences of n {\displaystyle n} distinct items that can be drawn from a universe of x {\displaystyle x} items. [ 97 ]
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
For most symbols, the entry name is the corresponding Unicode symbol. So, for searching the entry of a symbol, it suffices to type or copy the Unicode symbol into the search textbox. Similarly, when possible, the entry name of a symbol is also an anchor, which allows linking easily from another Wikipedia article. When an entry name contains ...
An alternative, the slashed zero (looking similar to the letter O except for the slash), was primarily used in hand-written coding sheets before transcription to punched cards or tape, and is also used in old-style ASCII graphic sets descended from the default typewheel on the Teletype Model 33 ASR.
Zero was not treated as a number at that time, but as a "vacant position". [39] Qín Jiǔsháo's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol ‘〇’ for zero. [40] The origin of this symbol is unknown; it may have been produced by modifying a square symbol. [41]
The plus and minus symbols are used to show the sign of a number. In mathematics, the sign of a real number is its property of being either positive, negative, or 0.Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign.
Symbol Name Date of earliest use First author to use ... factorial: 1808 Christian Kramp:
For example, the empty products 0! = 1 (the factorial of zero) and x 0 = 1 shorten Taylor series notation (see zero to the power of zero for a discussion of when x = 0). Likewise, if M is an n × n matrix, then M 0 is the n × n identity matrix , reflecting the fact that applying a linear map zero times has the same effect as applying the ...