Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter

    Let a_n be a sequence. If a_n -> b and a_n -> c then b = c.

    Is this fact useful? I mean, are there any proofs that two things are equal by showing that there exists a sequence which approaches both of them?
    • PS Helper

    PS Helper
    The thing with analysis topics like this is that although they might be fairly obvious and not very useful, if they weren't true it would be very not-useful, so you have to prove mathematically that they're true (because intuition isn't good enough). Uniqueness of a limit isn't necessarily obvious, hence the requirement that this be proved.

    It's probably more useful in cases where you're given, say, that x_n \to L (with L unknown), but if you know what the limit of the sequence x_n is then you can work out L by just setting it equal to the limit.
Have you ever experienced racism/sexism at uni?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.