the number 0.23571113....

Asked Jun 07 '21 at 13:23

Active Jun 07 '21 at 13:25

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So I was looking into infinite decimals that have patterns and trying to practice turning them into ratios (for example 0.1111...=1/9)

and then I thought of this number 0.23571113... with all the primes into infinity I think this number has a name probably related to Euler, if so I would like to know it.

my question is this number rational or irrational or hasn't been figured out yet?
if so please provide simple proof.

asked Jun 07 '21 at 13:23

oximas

https://math.stackexchange.com/questions/778695/prove-the-irrationality-of-0-235711131719 – pietfermat Jun 07 '21 at 13:26
3

It is irrational. See this post. As the concatenation of all prime numbers contains within it every natural number, your decimal expansion will never repeat. – JMoravitz Jun 07 '21 at 13:26
@JMoravitz how can we be sure that it does contain every natural number in it? – Prime Mover Jun 07 '21 at 13:28
@PrimeMover that is explained in the linked post. – JMoravitz Jun 07 '21 at 13:29
@JMoravitz oh yes, thanks. – Prime Mover Jun 07 '21 at 13:33
3

The Copeland–Erdős constant is irrational If it were rational, its decimal expansion would eventually be periodic – Henry Jun 07 '21 at 13:25

the number 0.23571113....

0 Answers0