The integer numbers are those that express a complete unit, so they do not have an integer part and a decimal part. Eventually whole numbers can be conceived as fractions whose denominator is the number one. For example: 430, 12, -1, -326.
When we are little they try to teach us the math with an approach to reality and they tell us that whole numbers represent what exists around us but cannot be divided (people, balls, chairs, etc.), while decimal numbers represent what can be divided in the way desired (sugar, water, distance to a place).
This explanation is somewhat simplistic and incomplete, since integers also include, for example, numbers. negative numbers, which escape this approach. Integers, moreover, belong to a larger category: they are rational, real, and complex.
Several integers are listed here as an example, also clarifying how they should be named with Spanish words:
- 430 (four hundred thirty)
- 12 (twelve)
- 2,711 (two thousand seven hundred and eleven)
- one (one)
- -32 (minus thirty-two)
- 1,000 (thousand)
- 1,500,040 (one million five hundred thousand and forty)
- -one (minus one)
- 932 (nine hundred thirty two)
- 88 (eighty-eight)
- 1,000,000,000,000 (a billion)
- 52 (fifty-two
- -1,000,000 (minus one million)
- 666 (six hundred sixty six)
- 7,412 (seven thousand four hundred twelve)
- 4 (four)
- -326 (minus three hundred twenty-six)
- fifteen (fifteen)
- 0 (zero)
- 99 (ninety nine)
Characteristics of integers
The whole numbers represent the most elementary tool of mathematical calculation. The simplest operations (such as addition and subtraction) can be done without problem with just knowing the integers, both positive and negative.
Furthermore, any operation involving integers will result in a number that also belongs to that category. The same goes for the multiplication, but not so with the division: In fact, any division involving both odd and even numbers (among many other possibilities) will necessarily result in a non-integer number.
The whole numbers have an infinite expanse, both forward (on a number line, to the right, adding more and more digits) and backward (to the left of that same number line, after passing through 0 and adding digits preceded by the “minus” sign.
Knowing the integers, one of the basic postulates of mathematics can be easily interpreted: ‘for any number, there will always be a greater number’, from which it follows that ‘for any number, there will always be infinitely greater numbers’.
On the contrary, the same does not happen with another of the postulates that demands the understanding of the fractional numbers: ‘between any two numbers, there will always be a number’. From the latter it also follows that there will be infinities.
As for its form of written expression, integers greater than a thousand are usually written by placing a period or leaving a thin space every three digits, starting from the right. This is different in the English language, in which commas are used instead of points to separate the units of a thousand, reserving the points precisely for numbers that include decimals (that is, non-integers).