Question about number sequences

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The discussion centers on the concept of infinite non-repeating number sequences, specifically addressing whether any finite number sequence will appear within such sequences, using the digits of pi as a reference. Participants clarify that while any finite sequence of digits will appear infinitely often in a normal number, the normality of pi has not been proven. Thus, the statement regarding the appearance of finite sequences in pi remains unverified. The distinction between infinite non-repeating sequences and normal numbers is crucial to understanding the topic.

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Is the following statement true or false, and why:

In an infinite non repeating number sequence (like the digits of pi), any given finite number sequence will appear in it.
 
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Galap said:
Is the following statement true or false, and why:

In an infinite non repeating number sequence (like the digits of pi), any given finite number sequence will appear in it.

I don't know what an "infinite non repeating number sequence" is. If a number sequence is a sequence of digits 0 through 9, a nonrepeating number sequence is a number sequence without repeated digits, and an "infinite non repeating number sequence" is an "infinite" "nonrepeating number sequence", then there are no infinite non repeating number sequences.

But going out on a limb here: if you instead mean a normal number, then any finite sequence of digits (in any base!) will appear infinitely often by definition. But we haven't proven that pi is normal, so we don't know that this is true for pi.
 
Yes. I was intending to mean normal number. I wasn't familiar with that terminology. Thanks.

Interesting that we haven't proved pi is normal...
 

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