Let A denote a non-empty set. Explain what we mean by a sequence of elements in set A.

Thanks!

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- April 5th 2007, 11:47 AMMathStudent1Definition of a sequence of elements in a set?
Let A denote a non-empty set. Explain what we mean by a sequence of elements in set A.

Thanks! - April 5th 2007, 11:57 AMJhevon
By "a sequence of elements in set A" we mean an ordered list of all the elements in A. That is, if we call the first element a_1, the second a_2, the third a_3 and so on, then the sequence of elements in set A is the sequence

{An}= a_1, a_2, a_3, a_4,....

for more on sequences see Sequence

- April 5th 2007, 12:00 PMThePerfectHacker
- April 5th 2007, 12:02 PMJhevon
Note that we can think of a sequence as a function with domain the natural numbers and range some subset of the real numbers. thinking about it that way, if we can find some function of n, where n represents the elements of the natural numbers, then An (that is A sub n), will be the formula for this sequence. plugging in n=1 into the function we get a_1, plugging in n=2 into the function we get a_2 and so on.

- April 5th 2007, 12:03 PMThePerfectHacker
I need to warn you. Our Analysis book, accepts that set N (natural numbers) are {1,2,3...}.

In fact, the standard notion of natural number includes zero as well.

This is why I used Z^+.

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And when you said "subset" you should have said "non-trivial subset". Again our book does never says that. - April 5th 2007, 12:11 PMJhevon