What are integers?

What is an integer?

integer or even relative integer, a number that can be expressed as the difference of two natural numbers (→ Z, set of integers). It can be positive (+1, +2, +3, ...; you can omit to write the + sign), negative (−1, −2, −3, ...) or null.

What are the integers?

• The integers (or relative integers or, simply, relative numbers) correspond to the set obtained by joining the natural numbers (0, 1, 2, ...) ...
• The integers are then defined exactly as the set of numbers that are the result of subtraction of natural numbers.

What are the integers from 1 to 100?

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... One of the main characteristics that must be remembered is that natural numbers are infinite; the list we have just written starts with zero and never ends! To convince you of this we can try to think of a very large number.

Why are they called natural numbers?

In common parlance, "cardinal numbers" are those used for counting and "ordinal numbers" are those used for sorting. The natural numbers correspond to the set {0, 1, 2, 3, 4,…}. They are made to correspond biunivocally to the set of non-negative integers {0, +1, +2, +3, +4,…}.

RELATIVE integers 1 introduction

What is the largest of the natural numbers?

Theorem: 1 is the largest natural number.

What are the prime numbers up to 100?

At the end of the job, the circled numbers are the prime numbers within 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

What are the integers from 1 to 21?

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc .. All OTHER natural integers are ODD. So they are odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, etc ..

How are positive integers represented?

Zero is also an integer, but it is not preceded by any sign. The numbers preceded by the plus sign are called positive numbers: +1, +2, +3, +4, +5, ..., and they are the numbers that the pupils now know very well. Numbers preceded by the minus sign are called negative numbers: ... -5, -4, -3, -2, -1.

What are non-integers?

Real numbers are nothing more than decimal numbers that can be represented by a succession of digits (i.e. symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9), a comma and a sign (- or +, and the latter is generally not written explicitly).

When is a number different from 0?

0 is less than any positive number, but greater than any negative number; all negative numbers are less than positive numbers; the greater number between two integers (positive) is the one with the greatest absolute value; the larger of two (negative) integers is the one with the smallest absolute value.

What is the set of negative numbers called?

The set consisting of N, the number 0 and all negative integers is called the set of relative integers, often called only integers, and is denoted by Z. The natural numbers N, considered as elements of Z, are called integers positive.

When is a number equal to 0?

A number is called "even" if it is an integer multiple of 2. As an example, the reason 10 is even is that it equals 5 × 2. Similarly, 0 is an integer multiple of 2, specifically 0 × 2 = 0, so 0 is even. It is also possible to explain why 0 is even without reference to formal definitions.

How do you get an integer?

You can write the whole number in a variety of ways. For example, write the integer in standard format (for example 63), extended form (for example 100 50 +2, which in the standard form would be 152) or in written form (like 1213).

What are real numbers?

Real numbers are numbers described by means of a limited or unlimited decimal representation, periodic or non-periodic, and they are all and only rational numbers and irrational numbers. The set of real numbers is indicated by the symbol ℝ. : completeness.

How to understand if a number is rational?

The rational numbers, indicated with the symbol ℚ, are all and only numbers that can be expressed in the form of a fraction with the numerator and denominator given by integers. Rational numbers also include integers as a subset, and are infinite.

How are integers and reals represented in a calculator?

The SETS THAT CAN BE REPRESENTED by a computer are 4 and more precisely they are: N = set of Natural numbers; Z = set of Relative numbers; Q = set of rational numbers; R = set of Real numbers, which are infinite and infinitely dense.

What is the absolute value of an integer?

The absolute value of a number is equal to the number itself if the number is positive or null, it is the opposite of the number if the number is negative.

How do you define the sum of two concordant integers?

Recall that two relative numbers are said to agree when they have the same sign. The sum of two concordant relative numbers is a relative number that has the same sign as the addends and the sum of their absolute values ​​as an absolute value.

Who Invented Integers?

Leopold Kronecker (Legnica, 7 December 1823 - Berlin, 29 December 1891) was a German mathematician and logician.

What is the sum of the numbers 20 to 100?

The answer, on the other hand, was immediate on the part of the child: 5050. How did he do it?

How do you find prime numbers?

Wanting to give a definition for prime numbers, we will say that: a number greater than 1 is prime if it is divisible only by 1 and by itself. Conversely, we can give a definition for composite numbers by writing that: a number greater than 1 is a composite number if it is not a prime number.

What are the prime numbers between 30 and 60?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

What is divisible by 187?

It is a composite number with 4 divisors: 1, 11, 17, 187.

How is the set of natural numbers indicated?

The first set that we will examine is the set of natural numbers. It is indicated by the letter N and its elements are positive integers, the first numbers, historically, to have been used by humanity: N = {1, 2, 3, 4. . . . .} Of course the elements of N: 1, 2, 3, 4. . . they are infinite.