<p>The Weierstrass Extreme Value Theorem guarantees this. However, it's used so frequently that economists take it for granted or omit it in graduate courses and research papers. MWG is a maturity book. Part of mathematical maturity is being able to fill in the details for a proof.</p>

CC BY-SA 3.0
2016-07-01T14:56:02.993Z
2016-07-01T14:56:02.993Z
ml0105
<p>This is just semantics, but MWG doesn't use the Weierstrass Theorem in its Math Appendix when using the fact that a continuous function always has a max value on any compact set.</p>

<p>Some books appeal directly to the Weierstrass Theorm.</p>

<p>Is there a right or wrong answer to this? Or is it more just, like I said, semantics?</p>

CC BY-SA 3.0
2016-06-29T07:12:36.600Z
Excuse me but what is your question?
Giskard
CC BY-SA 3.0
2016-06-29T19:15:13.233Z
The Weierstrass Extreme Value Theorem guarantees this. However, it's used so frequently that economists take it for granted or omit it in graduate courses and research papers sometimes. MWG is a maturity book. Part of mathematical maturity is being able to fill in the details for a proof.
ml0105
CC BY-SA 3.0
2016-07-01T13:02:54.523Z
@ml0105, thank you for the comment, that was exactly what I was looking for. Somethings are obvious to some and not to others haha!
Frank Swanton
CC BY-SA 3.0
2016-07-01T13:04:01.680Z
@ml0105, if you put that as answer, I will select it. This post will be useful to those who might been confused like me
Frank Swanton
CC BY-SA 3.0
2016-07-01T14:56:28.913Z
I've made my comment an answer. :-)
ml0105
<microeconomics><consumer-theory><choice-theory>
Weierstrass Thm: Continuous Fn Attaining Extrema on Compact Domain $u:\mathbb{R^L}\rightarrow\mathbb{R}$
Frank Swanton
# Weierstrass Thm: Continuous Fn Attaining Extrema on Compact Domain $u:\mathbb{R^L}\rightarrow\mathbb{R}$

(Asked by: username_0 on 2016-06-29)

This is just semantics, but MWG doesn't use the Weierstrass Theorem in its Math Appendix when using the fact that a continuous function always has a max value on any compact set.

Some books appeal directly to the Weierstrass Theorm.

Is there a right or wrong answer to this? Or is it more just, like I said, semantics?

**Tags:** microeconomics, consumer-theory, choice-theory

> **Comments:**
> **username_1**: Excuse me but what is your question?  
> **username_2**: The Weierstrass Extreme Value Theorem guarantees this. However, it's used so frequently that economists take it for granted or omit it in graduate courses and research papers sometimes. MWG is a maturity book. Part of mathematical maturity is being able to fill in the details for a proof.  
> **username_0**: @username_2, thank you for the comment, that was exactly what I was looking for. Somethings are obvious to some and not to others haha!  
> **username_0**: @username_2, if you put that as answer, I will select it. This post will be useful to those who might been confused like me  
> **username_2**: I've made my comment an answer. :-)  

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## 1 answers

### Answer by username_2 on 2016-07-01. Score: 2 | Accepted answer

The Weierstrass Extreme Value Theorem guarantees this. However, it's used so frequently that economists take it for granted or omit it in graduate courses and research papers. MWG is a maturity book. Part of mathematical maturity is being able to fill in the details for a proof.


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