"१ (संख्या)" च्या विविध आवृत्यांमधील फरक

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'''१''' ('''एक''') हा क्रमांक आहे.

 

One, sometimes referred to as '''unity''', is the [[integer]] before [[2 (number)|two]] and after [[0 (number)|zero]]. One is the first non-zero number in the [[natural number]]s as well as the first [[odd number]] in the natural numbers.

 

Any number multiplied by one is the number, as one is the [[Identity element|identity]] for multiplication. As a result, one is its own [[factorial]], its own [[Square (algebra)|square]], its own [[Cube (algebra)|cube]], and so on. One is also the [[empty product]], as any number multiplied by one is itself, which produces the same result as multiplying by no numbers at all.

 

[[चित्र:Evolution1glyph.svg|thumb|left]]

The glyph used today in the Western world to represent the number 1, a vertical line, often with a [[serif]] at the top and sometimes a short horizontal line at the bottom, traces its roots back to the [[Indian subcontinent|Indians]], who wrote 1 as a horizontal line, much like the [[Written Chinese|Chinese]] character [[一]]. The [[Gupta script|Gupta]] wrote it as a curved line, and the [[Nagari]] sometimes added a small circle on the left (rotated a quarter turn to the right, this 9-look-alike became the present day numeral 1 in the [[Gujarati language|Gujarati]] and [[Punjabi language|Punjabi]] scripts). The [[Nepali language|Nepali]] also rotated it to the right but kept the circle small.<ref>Georges Ifrah, ''The Universal History of Numbers: From Prehistory to the Invention of the Computer'' transl. David Bellos et al. London: The Harvill Press (1998): 392, Fig. 24.61</ref> This eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the [[Roman numeral]] <math>\mathrm{I}</math>. In some European countries (e.g., [[Germany]]), the little serif at the top is sometimes extended into a long upstroke, sometimes as long as the vertical line, which can lead to confusion with the glyph for seven in other countries. Where the 1 is written with a long upstroke, the number 7 has a horizontal stroke through the vertical line.

Many older typewriters do not have a separate symbol for ''1'' and use the lowercase ''l'' instead. It is possible to find cases when the uppercase ''J'' is used, while it may be for decorative purposes.

 

Mathematically, 1 is

* in [[arithmetic]] ([[algebra]]) and [[calculus]], the [[natural number]] that follows [[0 (number)|0]] and precedes [[2 (number)|2]] and the multiplicative [[identity (mathematics)|identity]] of the [[integer]]s, [[real number]]s and [[complex number]]s;

This power series converges and has finite value [[if and only if]], <math>| x | < 1</math>. <!-- Probably not needed, really should look at convergence theorem as there are other series that converge iff |x| < 1 -->

 

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[[चित्र:U+2673 DejaVu Sans.svg|50px|right|1 as a resin identification code, used in recycling]]

* The [[resin identification code]] used in recycling to identify [[polyethylene terephthalate]]