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If you want to learn about basic Number system in Maths, then check out this post carefully. I made a diagram to understand it so easily. This one image is enough to understand you number system.
The Natural Numbers:
The Whole Numbers:
The Integers:
The Rational Numbers:
The Irrational Numbers:
An irrational number is a number that cannot be written as a ratio (or fraction). In decimal form, it never ends or repeats. The ancient Greeks discovered that not all numbers are rational; there are equations that cannot be solved using ratios of integers.
is about 1.414, because , which is close to . But you'll never hit exactly by squaring a fraction (or terminating decimal). The square root of is an irrational number, meaning its decimal equivalent goes on forever, with no repeating pattern:
Other famous irrational numbers are the golden ratio, a number with great importance to biology:
(pi), the ratio of the circumference of a circle to its diameter:
and , the most important number in calculus.
Irrational numbers can be further subdivided into algebraic numbers, which are the solutions of some polynomial equation (like and the golden ratio), and transcendental numbers, which are not the solutions of any polynomial equation. and are both transcendental.
The Real Numbers:
The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers. The real numbers are “all the numbers” on the number line.
There are infinitely many real numbers just as there are infinitely many numbers in each of the other sets of numbers. But, it can be proved that the infinity of the real numbers is a bigger infinity.
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