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A ''simply normal number to base 10'' is a '''normal number to base 10''', if not only single digits appear with the frequency of 1/10 in the long run, but each sequence of two digits {00,01,02,... ,98,99} can be found with the frequency of 1/100, each sequence of three digits with a frequency of 1/1000, and in general, each sequence of ''n'' digits will appear with a frequency of approximately 10<sup>-n</sup> when looking up more and more decimal places.
A ''simply normal number to base 10'' is a '''normal number to base 10''', if not only single digits appear with the frequency of 1/10 in the long run, but each sequence of two digits {00,01,02,... ,98,99} can be found with the frequency of 1/100, each sequence of three digits with a frequency of 1/1000, and in general, each sequence of ''n'' digits will appear with a frequency of approximately 10<sup>-n</sup> when looking up more and more decimal places.
A ''simply normal number to base 10'' has to be irrational - otherwise, a sequence of digits of some given length has to repeat itself forever - while some other sequences of this length will not appear at all.
Again, this concept can be taken to other bases.
Again, this concept can be taken to other bases.
A number is called '''normal''', if it is normal for every base b.
A number is called '''normal''', if it is normal for every base b. It is unproven if [[pi|π]] is a normal number, but an analysis of the first trillion digits of π suggests that it is normal.<ref>https://phys.org/news/2016-03-pi-random-full-hidden-patterns.html</ref>
==See further==
==See further==
*[https://mathworld.wolfram.com/NormalNumber.html Normal Number] at [[Wolfram Math World]]
*[https://mathworld.wolfram.com/NormalNumber.html Normal Number] at [[Wolfram Math World]]
[[Category:Number Theory]]