> 
> (Taken from an old exam - no homework:)
> 
> 
> Prove that every convergent sequence of real numbers is bounded.
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> 
> 

It would be cruel if our professor would take a task like that in the exam because I rather prefer calculating than doing theory (in an exam where you haven't got much time to describe things..). But I'll be honest and say I dislike theory in general! :-)

Anyway, for the task, I really got no idea how to proof that but I'll give it a try...

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We know that if a sequence is convergent it has exactly ONE limit where the sequences (sry my English here) accumulate. So the sequence will have an upper bound or lower bound, based on the limit, thus it will be surely bounded if it's convergent sequence.

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Even if my proof is wrong (most likely..) I'd like to see a proof like mine, where you avoid using (complicated) maths symbols. Just using words any human can understand would be awesome! :-)

Of course a more formal proof is welcome too but not necessarily preferred ^.^