1 (number)

In mathematics, 1 is the multiplicative identity. It is sometimes called the "unity".[1] It is also the only number for which these special facts are true:

• Any number ${\displaystyle n}$ multiplied by 1 equals that number: ${\displaystyle n\times 1=n}$. For example, ${\displaystyle 7\times 1=7}$.
• Any number ${\displaystyle n}$ divided by 1 equals that number: ${\displaystyle n/1=n}$. For example, ${\displaystyle 7/1=7}$.
• Any number ${\displaystyle n}$, except 0, divided by itself equals 1: ${\displaystyle n/n=1}$. For example: ${\displaystyle 7/7=1}$.
• 1 cannot be divided by any other number bigger than itself so that the result is a natural number.

In mathematics, 0.999... is a repeating decimal that is equal to 1. Many proofs have been made to show this is correct.[2][3]

The number one is important for computer science, because the binary numeral system uses only 1s and 0s to represent numbers. In machine code and many programming languages, one means "true" (or "yes") and zero means "false" (or "no").

• In Germany and Austria, one is the grade for "very good". It is the best grade of six possible grades in Germany, and the best of five possible grades in Austria. In the Netherlands, one is the lowest grade, and ten the highest. In Poland, one is also the lowest grade, and the highest is six.
• In numerology, the number one is a symbol for everything (unity), the beginning, and God.

• Zero
• Mathematical constant

1. Weisstein, Eric W. "1". mathworld.wolfram.com. Retrieved 2020-09-22.
2. Byers, William (2007). How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics. Princeton UP. pp. 39–41. ISBN 978-0-691-12738-5.
3. Richman, Fred (December 1999). "Is 0.999... = 1?". Mathematics Magazine. 72 (5): 396–400. doi:10.2307/2690798. JSTOR 2690798. Free HTML preprint: Richman, Fred (June 1999). "Is 0.999... = 1?". Archived from the original on 2 September 2006. Retrieved 23 August 2006. Note: the journal article contains material and wording not found in the preprint.