I might be wrong off the starting bat here, but e can be defined in an infinite series *1/0! + 1/1! + 1/2! + … + 1/n! *

So, i was wondering, Does a number exist that:

-> Cannot be expressed as a fraction (Irrational)

-> Cannot be expressed as a polynomial (Transcendental)

-> Cannot be expressed by an infinite series following a **set rule** (???)

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What about non-computable numbers like Chaitin’s constant?