What is a negative integer?

Answer 1

Whole numbers less than zeroA negative integer is a negative whole number that is the opposite of a counting number. When we count, we start at 1 and count 1, 2, 3, etc. Negative integers are the opposite of those numbers: -1, -2, -3, and so on. Further explanationAn integer is a "whole number." It has no fractional part to it. A negative integer is simply an integer less than 0. A positive integer, on the other hand, is an integer greater than 0. Technically, 0 is neither positive nor negative. Abstract but correct idea for IntegersThe Integers:

Most definitions of integers presuppose a numeric set, from which integers can be selected based on some predicate (e.g. logical condition). However, one can give a pure constructive definition. That is, we can create objects, which behave exactly as integers with respect to the basic arithmetic operations defined on the integers

Let N be the set of natural numbers. Let (a,b) and (a',b') be ordered pairs from the Cartesian product N x N. First, we define a relation ~rz on N x N by saying that (a,b) is related to (a',b') iff a + b' = a' + b. Written more technically:

(a,b) ~/rz (a',b') :<=> a + b' = a' + b

Then this relation is an equivalence relation (can easily be proven). Then

Z := N x N/rz

If [(a,b)] and [(a', b')] denote the equivalence classes containing (a, b) and (a', b'), respectively, and if we define addition and multiplication of those equivalence classes as:

1. [(a,b)] + [(a',b')] = [(a + a', b + b')]

2. [(a,b)] * [(a', b')] = [(a * b' + b * a', a * a' + b * b')]

then these operations are well-defined and the resulting set of all equivalence classes has all of the familiar properties of the integers (it therefore serves to define the integers based only on the natural numbers).

In this setting, a negative integer is an equivalence class, such that its representatives are of the form (a,b) with the property "b > a", where a, b are natural numbers.

Examples in this representation:

(-3) = [(3,0)] = [(8,5)]

(0) = [(0,0)] = [(137,137)]

(5) = [(0,5)] = [(17,22)]

Easy Ideas for Negative Integersnegative integers:= {y: x+y=0 for any positive integer x}

This means that if there is a natural number (the ones you use for counting) or the number zero then the negative integers are all the ones you can add to them to make a sum equal zero. example: 4+(-4)=0

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its anything with a - on it. it means that it is not a positive number, a number with a vaule less than 0
Any number below 0.
An integer is a whole number - a number without decimals. Negative means less than zero. Negative number have a minus sign in front of them. So, the negative integers are the numbers:

-1, -2, -3, -4, -5, -6, etc.

Answer 2

An integer is a whole number - a number without decimals. Negative means less than zero. Negative number have a minus sign in front of them. So, the negative integers are the numbers:

-1, -2, -3, -4, -5, -6, etc.