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How Counting Works?

Decimal

The number-system was ofcourse not given by god. It is us who defines a system to count. Hence we defined some rules to give meaning to it.

Since the most commonly used base system is decimal, we will use this number system to explain the concept.

When there is no object, the count is 0. Or write it as 00000 or 0000000 or ......00000000. The zeros, trailing towards left, doesn't signify anything, for any Base/radix system.

  • The initial count is : (..00)10

  • Count 1 object : Increase the digit. The number becomes (..01)10 .

  • Count 1 more object : Increase the digit. The number becomes (..02)10 .

  • Count 1 more object : Increase the digit. The number becomes (..03)10 .

  • Count 1 more object : Increase the digit. The number becomes (..04)10 .

  • Count 1 more object : Increase the digit. The number becomes (..05)10 .

  • Count 1 more object : Increase the digit. The number becomes (..06)10 .

  • Count 1 more object : Increase the digit. The number becomes (..07)10 .

  • Count 1 more object : Increase the digit. The number becomes (..08)10 .

  • Count 1 more object : Increase the digit. The number becomes (..09)10 .

  • Count 1 more object : Since it is Base-10 number system, we used all 10 unique digits to count objects.

    "When the current digit is the last digit of the base-system, to continue the counting, we make the current digit zero and increase the digit, just left to it, by 1. Repeat this process towards left.".

    The number becomes (..010)10 .

    But then again continue with same digit.

  • Count 1 more object : Increase the digit. The number becomes (..011)10 .

  • Count 1 more object : Increase the digit. The number becomes (..012)10 .

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  • Count 1 more object : Increase the digit. The number becomes (..019)10 .

  • Count 1 more object :

    When the current digit is the last digit of the base-system, to continue the counting, we make the current digit zero and increase the digit, just left to it, by 1. Repeat this process towards left.

    The number becomes (..020)10 .

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  • Count 1 more object : Increase the digit. The number becomes (..099)10 .

  • Count 1 more object :

    When the current digit is the last digit of the base-system, to continue the counting, we make the current digit zero and increase the digit, just left to it, by 1. Repeat this process towards left.

    The number becomes (..0100)10 .

  • Count 1 more object : Increase the digit. The number becomes (..0101)10 .

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  • Count 1 more object : Increase the digit. The number becomes (..0109)10 .

  • Count 1 more object :

    When the current digit is the last digit of the base-system, to continue the counting, we make the current digit zero and increase the digit, just left to it, by 1. Repeat this process towards left.

    The number becomes (..0110)10 .

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  • Count 1 more object : Increase the digit. The number becomes (..0129)10 .

  • Count 1 more object :

    When the current digit is the last digit of the base-system, to continue the counting, we make the current digit zero and increase the digit, just left to it, by 1. Repeat this process towards left.

    The number becomes (..0130)10 .

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  • Count 1 more object : Increase the digit. The number becomes (..0999)10 .

  • Count 1 more object :

    When the current digit is the last digit of the base-system, to continue the counting, we make the current digit zero and increase the digit, just left to it, by 1. Repeat this process towards left.

    The number becomes (..01000)10 .

And this continues till infinity.