<p>This is a definition. Definitions are always iff.</p>

<p>Consider this property. From now on we call this and exactly this (name of the concept here).</p>

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2017-10-17T07:39:08.570Z
Thank you @denesp. I was not sure if it was a definition or condition.
eigenvector
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2017-10-17T07:44:13.750Z
@eigenvector That is strange because you yourself wrote "definition" twice.
Giskard
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2017-10-17T07:59:47.340Z
Fair point. Note, though, that I also wrote: "condition (or definition?) once in the last paragraph. Anyway, lets agree that my wording was not very precise. :-) My understanding is still confused. Let me rephrase my question: Is what I wrote above a definition or is it a condition?
eigenvector
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2017-10-17T10:05:00.450Z
@eigenvector As I said in my answer it is the definition.
Giskard
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2017-10-17T07:22:49.630Z
2017-10-17T07:22:49.630Z
Giskard
<p>I have a question about the following definition of a continuous preference relation. I apologize for not providing a reference and will try to add one as soon as I can find one.</p>

<p>Definition:</p>

<p>A preference relation is continuous <strong>if</strong> for all sequences x_n, y_n with x_n converges to x and y_n converges to y as n goes to infinity and x_n is at least as good as y_n for all n, then this must also hold for the limits x and y.</p>

<p>My simple question is:
Is the <strong>if</strong> an iff or only an if? That is, say this condition (or definition?) above is not ful-filled, can I infer that the preference relation is not continuous or might it still be continuous?</p>

<microeconomics><preferences>
Continuity of preference relation (iff?)
eigenvector
# Continuity of preference relation (iff?)

(Asked by: username_0 on 2017-10-17)

I have a question about the following definition of a continuous preference relation. I apologize for not providing a reference and will try to add one as soon as I can find one.

Definition:

A preference relation is continuous **if** for all sequences x\_n, y\_n with x\_n converges to x and y\_n converges to y as n goes to infinity and x\_n is at least as good as y\_n for all n, then this must also hold for the limits x and y.

My simple question is:
Is the **if** an iff or only an if? That is, say this condition (or definition?) above is not ful-filled, can I infer that the preference relation is not continuous or might it still be continuous?

**Tags:** microeconomics, preferences

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## 1 answers

### Answer by username_1 on 2017-10-17. Score: 3 | Accepted answer

This is a definition. Definitions are always iff.

Consider this property. From now on we call this and exactly this (name of the concept here).

> **Comments:**
> **username_0**: Thank you @denesp. I was not sure if it was a definition or condition.  
> **username_1**: @eigenvector That is strange because you yourself wrote "definition" twice.  
> **username_0**: Fair point. Note, though, that I also wrote: "condition (or definition?) once in the last paragraph. Anyway, lets agree that my wording was not very precise. :-) My understanding is still confused. Let me rephrase my question: Is what I wrote above a definition or is it a condition?  
> **username_1**: @eigenvector As I said in my answer it is the definition.  

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