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Analysis sequence help!

Please help I have no idea :smile:
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Original post by chloeaj95
Please help I have no idea :smile:

what's the definition of lim a_n =1?
Reply 2
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chloeaj95
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Original post by Shillington
what's the definition of lim a_n =1?


I have no idea I've missed a lot of lectures due to being ill, and can't find that in my notes,
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ztibor
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Original post by chloeaj95
Please help I have no idea :smile:


Start with the definition of lim a_n=1, then
choose a proper epsilon (e. g 1/2)
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chloeaj95
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Original post by ztibor
Start with the definition of lim a_n=1, then
choose a proper epsilon (e. g 1/2)


What's the definition of it?
Original post by chloeaj95
What's the definition of it?

The limit of a sequence a_n is x IF for all epislion > 0 there exists a natural number N such that |a_n-x|<epsilon for all n>N. What it's saying is that no matter how small the distance from x, there exists a number N such that for all a_n after a_N, the distance from a_n to x is less than epsilon.
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davros
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Original post by Shillington
The limit of a sequence a_n is x IF for all epislion > 0... .


That is a brilliant new word :smile:
Reply 7
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BlueSam3
17
And a LaTeX-ed up version:


(an)→a∈R(a_n) \to a \in \mathbb{R} iff ∀ε>0,∃Nε∈N\forall \varepsilon > 0, \exists N_\varepsilon \in \mathbb{N} such that ∀n>Nε,∣an−a∣<ε\forall n > N_\varepsilon, |a_n - a| < \varepsilon.

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