Extreme Value Theorem true for constants?

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The discussion centers on the application of the Extreme Value Theorem to constant functions, with one participant expressing skepticism about its validity. They argue that while every point in a constant function can be considered both a maximum and minimum, this seems unsatisfactory. Another participant clarifies that the theorem simply states that a continuous function on a closed interval will have a minimum and maximum, which can indeed be the same for constants. Despite acknowledging the logic, the original poster remains dissatisfied with the concept. The conversation highlights a tension between mathematical definitions and personal perceptions of their implications.
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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?
 
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Constant functions are continuous, I don't really understand what your issue is. Can you elaborate about why this is bs?
 
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.
 
Austin said:
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.
 
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.
 
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?
 
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.
 
But I do see what you're saying and I appreciate your logic. Thank you.
 
Hmm, Alright.
 
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Did you get my message?
 

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