Extreme Value Theorem true for constants?

[member 508213]

My textbook says the extreme value theorem is true for constants but I don't buy it. I mean I suppose that every value over a closed interval for a constant would be a maximum and a minimum technically but it seems like BS to me. Can anyone explain why this BS is true?

 

[Jorriss]

Constant functions are continuous, I don't really understand what your issue is. Can you elaborate about why this is bs?

 

[member 508213]

No, my problem is the extreme value theorem says that for a continuous function on a closed interval there will be a minimum and maximum value. My complaint with that is for a constant every point is a minimum and a maximum and I just think that is pretty lame so I'm mad.

 

[Jorriss]

My complaint with that is for a constant every point is a minimum and a maximum and I just think that is pretty lame so I'm mad.

Well, okay then.

 

[member 508213]

Well thanks for your answer, my problem isn't with my understanding of it I just don't really like it. However, your point about the theorem saying that the function must simply have a min and max makes sense, I suppose that the min and max don't have to be different and not be at every point; I still don't like it though.

 

[Jorriss]

As a follow up question, how would you define the maximum and minimum of a function? Do you know the definition or do you just find it is not pleasing to how one thinks about maximum and minimum?

 

[member 508213]

Max= highest value the function reaches
Min= lowest value a function reaches

So for a constant yes they would have both technically. Like I said I just think it's poop.

 

[member 508213]

But I do see what you're saying and I appreciate your logic. Thank you.

 

[Jorriss]

Hmm, Alright.

 

[member 508213]

Did you get my message?