Defintions of LH limit and RH limit

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MSI_10
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#1
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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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Implication
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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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MSI_10
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(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".
Name:  LH RH Limit.png
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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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Jarred
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These are the definitions I always went with:

A function f : (c, a) \rightarrow \mathbb{R} has a right hand limit l at c if:
for any \varepsilon &gt; 0 there exists a \delta &gt; 0 such that for all x \in (c, a) with c &lt; x &lt; c+\delta we have |f(x) - l| &lt; \varepsilon

And relatedly:

A function f : (b,c) \rightarrow \mathbb{R} has a left hand limit l at c if:
for any \varepsilon &gt; 0 there exists a \delta &gt; 0 such that for all x \in (a, c) with c-\delta &lt; x &lt; c we have |f(x) - l| &lt; \varepsilon
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BlueSam3
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(Original post by Jarred)
These are the definitions I always went with:

A function f : (c, a) \rightarrow \mathbb{R} has a right hand limit l at c if:
for any \varepsilon &gt; 0 there exists a \delta &gt; 0 such that for all x \in (c, a) with c &lt; x &lt; c+\delta we have |f(x) - l| &lt; \varepsilon

And relatedly:

A function f : (b,c) \rightarrow \mathbb{R} has a left hand limit l at c if:
for any \varepsilon &gt; 0 there exists a \delta &gt; 0 such that for all x \in (a, c) with c-\delta &lt; x &lt; c we have |f(x) - l| &lt; \varepsilon
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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Jarred
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(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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