# Defintions of LH limit and RH limit

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#1
In my uni's lecture notes, they define the Left Hand Limit as:

The point x0 (belonging to the set of real numbers) is called the LH limit point of a number set X(belonging to the set of real numbers) if any neighbourhood of the point contains at least one x belonging to the set X such that x<x0

it then says that the definition for the Right hand limit is ''very similar'' but doesn't attempt to show the difference.

Am I correct in thinking that the difference would be what is in bold from above i.e instead of x<x0 is it x>x0 instead?
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7 years ago
#2
It's hard for me to understand what you've written since I think you are missing some curly brackets and otherwise confusing mathematical notation.. but I want to say "yes, you are correct".
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#3
(Original post by Implication)
It's hard for me to understand what you've written since I think you are missing some curly brackets and otherwise confusing mathematical notation.. but I want to say "yes, you are correct".

R= Real numbers, s.t=such that..

is that better? I am literally just typing up all definitions from semester 1 and that's how my lecturer defined them word by word..
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7 years ago
#4
These are the definitions I always went with:

A function has a right hand limit at if:
for any there exists a such that for all with we have

And relatedly:

A function has a left hand limit at if:
for any there exists a such that for all with we have
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7 years ago
#5
(Original post by Jarred)
These are the definitions I always went with:

A function has a right hand limit at if:
for any there exists a such that for all with we have

And relatedly:

A function has a left hand limit at if:
for any there exists a such that for all with we have
He's talking about left and right limits of subsets of the reals, what you'd probably call an infimum and supremum, not limits of functions.
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7 years ago
#6
(Original post by BlueSam3)
He's talking about left and right limits of subsets of the reals, what you'd probably call an infimum and supremum, not limits of functions.
Darn it, I think tonight I shall probably get more sleep and actually try to read things properly
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