Pi (π) contains infinitely many integers when expressed in its decimal representation.
Pi is an irrational number, which means it cannot be expressed as a simple fraction p/q, where p and q are integers. Its decimal representation is non-terminating and non-repeating. Because of this, within the infinite sequence of digits after the decimal point, you will find an infinite number of integer sequences of any length.
Consider the following:
- Pi's Value: Pi is approximately 3.1415926535...
- Integers After the Decimal: The digits after the "3." form an infinite, non-repeating sequence. Any finite sequence of digits can be considered an integer if you truncate the digits after it. For example, 1, 14, 141, 1415, 14159, and so on, are all integers found within pi's decimal expansion. Since the expansion is infinite, so is the number of these integers.
Therefore, although Pi itself is not an integer, its decimal representation contains an infinite number of integers. These integers are found within the infinite string of digits following the decimal point.
