Question about number sequences

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In summary, the statement that in an infinite non repeating number sequence, any given finite number sequence will appear is true for normal numbers, but it has not been proven for pi.
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Galap
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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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  • #2
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.
 
  • #3
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...
 

FAQ: Question about number sequences

What is a number sequence?

A number sequence is a list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term.

What are the different types of number sequences?

There are various types of number sequences, including arithmetic, geometric, and Fibonacci. In an arithmetic sequence, the difference between each term is constant. In a geometric sequence, the ratio between each term is constant. A Fibonacci sequence is a series of numbers where each term is the sum of the two previous terms.

How do you find the next term in a number sequence?

To find the next term in a number sequence, you need to identify the pattern or rule that the sequence follows. Once you have identified the pattern, you can use it to generate the next term in the sequence.

What is the importance of number sequences?

Number sequences are important in mathematics and science as they help us understand patterns and relationships between numbers. They also have practical applications in fields such as finance, computer programming, and data analysis.

How can number sequences be used in problem-solving?

Number sequences can be used in problem-solving to find missing terms, predict future values, and identify patterns. They can also help in solving more complex mathematical problems by breaking them down into smaller, more manageable steps.

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