# Maximum, Minimum, Supremum and Infimum

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#1

I did the following:

what is maximum and minimum? and how comes the correct answer is:

0
7 years ago
#2
Hi raees, -2 is not an supremum of the whole set, it's only an infimum of the elements of set that are less than zero. A supremum has to be greater than or equal to all the elements of the set. It is not greater than or equal to 10, for example, which is in the set. There is no supremum as the set is unbounded above (i.e. for any real number there is some bigger number in the set).

Similarly for the infimum part (and minimum and maximum).

Hope that helps!
1
7 years ago
#3
(Original post by raees)

I did the following:

what is maximum and minimum? and how comes the correct answer is:

THe maximum is the greatest, the minimum is the least element in the set.
Your work is true only for one and another subset of z
THE set of z is \[-2,3]
1
#4
thank you, I get it ^_^
0
6 years ago
#5
HELLO,
Thank you for your thoughtful response giving your definition of supremum. Definitions are a very important part of any mathematicians' thought and work. I happened on this web page as a good friend of my who is sometimes impatient with mathematics and with good reason being a medical doctor became engaged with my discussing integer number sequences. I was thinking of a problem and conjecture from number theory involving the Primes, composite numbers, isolate integer bounds, and Prime number cycles and so on. Well, I contended my medical friend would not guess a number sequence as Prime but only as odd. I was right, and we happily continued onward looking at low positive integer sequences and some short integer measure Prime Cycles. I chose 15 as the max sequence value and used the term supremum. For my friend's edification and learning, I searched, found this page, and forwarded it to my friend.

Truly yours, from New York City in the United States, Dr. ELYAS FRAENKEL ISAACS; PHD, DPH, DDiv., MD(res)
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