Draft:Gaussian symbol
Submission declined on 18 March 2021 by Dan arndt (talk).
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Submission declined on 27 November 2020 by KylieTastic (talk). This submission is not adequately supported by reliable sources. Reliable sources are required so that information can be verified. If you need help with referencing, please see Referencing for beginners and Citing sources. This draft's references do not show that the subject qualifies for a Wikipedia article. In summary, the draft needs multiple published sources that are: Declined by KylieTastic 3 years ago.
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Submission declined on 16 July 2020 by Eternal Shadow (talk). This submission is not adequately supported by reliable sources. Reliable sources are required so that information can be verified. If you need help with referencing, please see Referencing for beginners and Citing sources. Declined by Eternal Shadow 4 years ago. |
Submission declined on 10 July 2020 by Flori4nK (talk). This submission is not adequately supported by reliable sources. Reliable sources are required so that information can be verified. If you need help with referencing, please see Referencing for beginners and Citing sources. Declined by Flori4nK 4 years ago. |
- Comment: Fails WP:GNG, requires significant coverage in multiple independent secondary sources. Dan arndt (talk) 09:46, 18 March 2021 (UTC)
- Comment: Wikis are not valid sources, use any sources directly KylieTastic (talk) 10:57, 27 November 2020 (UTC)
It has been suggested that Floor_(programming) be merged into this page. (Discuss) |
The Gaussian symbol is a mathematical symbol in the form of square brackets \lbrack x\rbrack , indicating the largest integer not greater than (equal to or less than) the number x, that is, .
The Gaussian symbol first appeared in Gaussian mathematics "Arithmetic Research".
Operation example: .
In computer science, the Gaussian symbol is often expressed as the INT() function.
Later, in 1962, Kenneth Iverson called the Gaussian symbol in his book A Programming Language (,floor) and introduced it at the same time. Take the top symbol (,ceil) (used to represent the smallest of the integers not less than x).
Some properties of Gaussian symbols
[edit]If and only if x is an integer, the "equals" sign on the left holds.
- For all real numbers x, there are:
- When n is a positive integer, there are:
- When x and n are positive numbers, there are:
- For any integer k and any real number x, there are:
- If x is a real number and n is an integer, we have if and only if .
- Using the Gaussian notation, many prime formulas can be generated (but have no practical use).
- For non-integer real numbers x, the Gaussian function has the following Fourier series expansion:
- If m and n are positive prime numbers that are relatively prime, then:
- According to Beatty's theorem, every positive irrational number can be divided into a set of integers by Gaussian notation.
- For each positive integer k, the representation under p carry is digit.
References
[edit]
1. Carl Friedrich Gauss (1798). Disquisitiones Arithmeticae.
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