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'''[[Pi]] contains pi''' as showing by proof proved by [[induction]]:

Stated another way, no one disputes that pi includes every number that has a finite representation. Thus pi includes itself in all of its increasingly precise representations, without limit, and therefore pi contains pi itself within a vanishingly small margin of error. == Numeric series without termination == Pi has no termination in its digital representation, no patterns in the digits, and no repetitive periodicity. Pi containing pi can be viewed as two strings: the original pi without termination in its digital representation, and another pi that starts within pi but also without any termination point. == Periodicity == Pi containing pi means that there will be a string of numbers that repeat themselves: from the beginning of pi to when it first begins to repeat itself, which then would repeat itself again and again. However, it is generally assumed that there are no repeating patterns in pi. The flaw in this argument against pi containing pi is that the periodicity may not occur until after an [[infinite]] string of digits, and thus this creates no contradiction with pi being an [[irrational number]]. == Analogy to Life and Eternity == Stumbling into the "pi within pi" amid another otherwise random string of numbers can seem eerily similar to happening upon [[eternity]] in [[heaven]] or [[hell]]. While the math question has a math answer, the implications for the existence of eternity are unmistakable. == See also == *[[Infinity denial]]*[https://math.stackexchange.com/questions/1608060/does-pi-contain-itself Stack Exchange commentary, arguing for "yes"]*[https://www.reddit.com/r/explainlikeimfive/comments/1zm55o/eli5_does_pi_contain_itself/ Reddit commentary, with a consensus of "no"]