Is there any natural number which has no successor? Is there a last number?

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Detailed Solution

A number tells us how many times a unit is contained in a given quantity.

Types of Number Systems:

Decimal Number System:

Uses digits 0 to 9 to represent numeric values. Numbers in the decimal system are called real numbers.

Classification of Real Numbers:

Rational Numbers: Can be expressed as a fraction.
- Integers: Whole numbers including positive, negative, and zero.
  - Positive integers
  - Negative integers
  - Whole numbers (0 and positive integers)
  - Natural numbers (starting from 1)
- Non-integer rational numbers (fractions that are not whole numbers)
Irrational Numbers: Cannot be expressed as fractions.

Natural Numbers:

Numbers starting from 1 with no fraction, used for counting. Denoted by N = {1, 2, 3, …}

Successor:

The number that comes immediately after a given number.

To find the successor of a number a:

S(a) = a + 1

Example: Successor of 4 is 5. Every natural number has a successor because natural numbers continue indefinitely.

Predecessor:

The number that comes immediately before a given number.

To find the predecessor of a number n:

P(n) = n - 1

Example: Predecessor of 5 is 4. The first natural number, 1, has no predecessor because 0 is not a natural number.