Maximum, Minimum, Supremum and Infimum

Watch
raees
Badges: 0
Rep:
?
#1
Report Thread starter 7 years ago
#1
Can someone please help with this:

Name:  Capture.PNG
Views: 407
Size:  3.8 KB

I did the following:

Name:  Capture.PNG
Views: 526
Size:  76.9 KB

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

Name:  Capture.PNG
Views: 263
Size:  1,021 Bytes
0
reply
valori
Badges: 0
Rep:
?
#2
Report 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
reply
ztibor
Badges: 10
Rep:
?
#3
Report 7 years ago
#3
(Original post by raees)
Can someone please help with this:

Name:  Capture.PNG
Views: 407
Size:  3.8 KB

I did the following:

Name:  Capture.PNG
Views: 526
Size:  76.9 KB

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

Name:  Capture.PNG
Views: 263
Size:  1,021 Bytes
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 z \in \mathbb R\[-2,3]
1
reply
raees
Badges: 0
Rep:
?
#4
Report Thread starter 7 years ago
#4
thank you, I get it ^_^
0
reply
DrElyasFIsaacs
Badges: 0
Rep:
?
#5
Report 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)
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Should there be a new university admissions system that ditches predicted grades?

No, I think predicted grades should still be used to make offers (639)
33.51%
Yes, I like the idea of applying to uni after I received my grades (PQA) (805)
42.21%
Yes, I like the idea of receiving offers only after I receive my grades (PQO) (377)
19.77%
I think there is a better option than the ones suggested (let us know in the thread!) (86)
4.51%

Watched Threads

View All
Latest
My Feed