Understanding Sequences with Finitely Many Terms of 1

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In summary, the conversation discusses the meaning of a set A consisting of sequences with the majority of their terms being 1, with the exception of a finite number of terms. This concept is commonly seen in mathematics.
  • #1
pivoxa15
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Homework Statement


What does this mean:
Set A consists of those sequences all but finitely many of whose terms are 1.






The Attempt at a Solution


In set A every sequence constains 1 somewhere but only finitely many terms are 1.
 
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  • #2
It means if a sequence is in A, only finitely many of its entries aren't '1'.

E.g. (1,0,1,2,1,1,1,1,1,1,...) is in A, but (1,1,0,0,0,0,0,...) and (0,2,4,6,...) aren't.
 
  • #3
pivoxa15 said:

Homework Statement


What does this mean:
Set A consists of those sequences all but finitely many of whose terms are 1.






The Attempt at a Solution


In set A every sequence constains 1 somewhere but only finitely many terms are 1.

Your statement is pretty much the opposite of what you are given! The original statement is "all but finitely many terms are 1" while your statement says all but finitely many are 1.
 
  • #4
HallsofIvy said:
Your statement is pretty much the opposite of what you are given! The original statement is "all but finitely many terms are 1" while your statement says all but finitely many are 1.

tricky, tricky.

Now I understand these statements. It occurs often in mathematics.
 

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