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The word integer comes from the Latin integer meaning "whole" or (literally) "untouched", from in ("not") plus tangere ("to touch"). "Entire" derives from the same origin via the French word entier, which means both entire and integer. [9] Historically the term was used for a number that was a multiple of 1, [10] [11] or to the whole part of a ...
The negative of a positive integer is defined as a number that produces 0 when it is added to the corresponding positive integer. Negative numbers are usually written with a negative sign (a minus sign). As an example, the negative of 7 is written −7, and 7 + (−7) = 0.
For example: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".
For example, + and () = + define the function that associates to each number its square plus one. An expression with no variables would define a constant function . In this way, two expressions are said to be equivalent if, for each combination of values for the free variables, they have the same output, i.e., they represent the same function.
Apart from division by zero being undefined, the quotient is not an integer unless the dividend is an integer multiple of the divisor. For example, 26 cannot be divided by 11 to give an integer. Such a case uses one of five approaches: Say that 26 cannot be divided by 11; division becomes a partial function.
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers.Integral data types may be of different sizes and may or may not be allowed to contain negative values.
In computer science, an integer literal is a kind of literal for an integer whose value is directly represented in source code.For example, in the assignment statement x = 1, the string 1 is an integer literal indicating the value 1, while in the statement x = 0x10 the string 0x10 is an integer literal indicating the value 16, which is represented by 10 in hexadecimal (indicated by the 0x prefix).
Repunits are integers that are represented with only the digit 1. For example, 1111 (one thousand, one hundred and eleven) is a repunit. Repdigits are a generalization of repunits; they are integers represented by repeated instances of the same digit. For example, 333 is a repdigit. The primality of repunits is of interest to mathematicians. [21]