# Supremum of a Monotonically Decreasing Sequence

• Nov 13th 2012, 09:42 AM
Math150
Supremum of a Monotonically Decreasing Sequence
Just a quick question to help me with this Calc/Analy proof. Is the supremum of a monotonically decreasing sequence equal to the first term in the sequence?
• Nov 13th 2012, 09:53 AM
Plato
Re: Supremum of a Monotonically Decreasing Sequence
Quote:

Originally Posted by Math150
Is the supremum of a monotonically decreasing sequence equal to the first term in the sequence?

Well \$\displaystyle \forall n\ge 2\$ we have \$\displaystyle a_1>a_n\$ for a decreasing as opposed to non-increasing sequences.
• Nov 13th 2012, 10:04 AM
Math150
Re: Supremum of a Monotonically Decreasing Sequence
Sorry, I'm a bit confused by that lol. I think I'd be better off showing the whole problem to give some context, Plato could I pm you because if I give more detail it might veer out of Calculus territory
• Nov 13th 2012, 10:44 AM
Plato
Re: Supremum of a Monotonically Decreasing Sequence
Quote:

Originally Posted by Math150
Sorry, I'm a bit confused by that lol. I think I'd be better off showing the whole problem to give some context, Plato could I pm you because if I give more detail it might veer out of Calculus territory

Post it here so all can see the question.