Assignment : Types of numbers in number theory

Pi π=3.141592653589793238462643383279502884197 having 39 decimal places

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AOA, In this 15-minute lecture, all the previous concepts are covered in a very good way.

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Type of Number Definition and Properties Natural Numbers Positive integers, excluding zero: 1, 2, 3, ... Whole Numbers Natural numbers and zero: 0, 1, 2, 3, ... Integers Positive and negative whole numbers, including zero: ..., -3, -2, -1, 0, 1, 2, 3, ... Rational Numbers Numbers are expressible as a ratio (fraction) of two integers: 1/2, -3/4, 7, 3/1, ... Irrational Numbers Numbers that cannot be expressed as a simple fraction: √2, π, e, ... Real Numbers All numbers on the real number line, including rationals and irrationals. Imaginary Numbers Numbers of the form "bi," where "b" is a real number and "i" is the imaginary unit (i^2 = -1). Example: 3i Complex Numbers Numbers of the form "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit. Example: 2 + 4i Prime Numbers Natural numbers greater than 1 that have exactly two distinct positive divisors (1 and themselves). Examples: 2, 3, 5, 7, 11, ... Composite Numbers Natural numbers greater than 1 that have more than two distinct positive divisors. Example: 4, 6, 9, 10, ... Perfect Numbers Natural numbers that are equal to the sum of their proper divisors. Example: 28 (1 + 2 + 4 + 7 + 14 = 28) Amicable Numbers Pairs of natural numbers where the sum of the proper divisors of each number equals the other. Example: (220, 284) Palindromic Numbers Numbers that read the same forwards and backward. Example: 121, 1331, 7777 Fibonacci Numbers A sequence of numbers where each number is the sum of the two preceding ones. Example: 0, 1, 1, 2, 3, 5, 8, ... Triangular Numbers Numbers that can be arranged in the shape of an equilateral triangle. Example: 1, 3, 6, 10, 15, ... Mersenne Primes Prime numbers can be written in the form 2^n - 1, where "n" is also a prime number. Example: 3, 7, 31, ... Fermat Primes Prime numbers that can be written in the form 2^(2^n) + 1. Examples: 3, 5, 17, 257, ... Perfect Powers Numbers that can be expressed as an integer raised to a positive integer power. Example: 8 (2^3), 27 (3^3), ...

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