What is the “Real Number” System?
In: Mathematics
Numbers in math are divided into a couple different classes (or as mathematicians call them, sets). Grade school tends to loop all of them together but higher level math does differentiate between them.
First there are the natural numbers. These are the numbers 0?, 1, 2, 3, 4, etc. All the numbers you would count with, in fact the only reason they exist is because of this idea of counting. This is commonly denoted with the letter N.
Then there are the integers. These are the natural numbers but we add the idea of negative into them. So …-3, -2, -1, 0, 1, 2, 3. Commonly noted with the letter Z.
Next we have the rationals (think ratio). These are the numbers that can be represented as a fraction of two integers numbers. There are infinitely many of them so its difficult to order them. Commonly denoted with the letter Q.
Finally we have the reals. This is all “normal numbers,” this includes the rational numbers but also numbers that include things like the square root of two, which is not rational, there is pi which is also not rational. Anything that can be represented as an infinite decimal also fits here. This is commonly denoted with the letter R.
There are a number of other subclasses of numbers sometimes useful, the prime numbers, transcendentals, etc. But its mostly these that are denoted.
Real numbers are all of the numbers that can be drawn on a number line. Positive, negative, zero, fractions, decimals, irrational numbers like pi or e…
The only numbers that aren’t real numbers are the imaginary numbers.
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