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/sci/ - Science & Math

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7297038 No.7297038 [Reply] [Original]

this shit don't make no fucking sense

>> No.7297140

>>7297038
An upper bound is a limit while a maximum needs to be a member of the set in question.

What's the problem? Seems fine to me.

>> No.7297169

[0,2] has a maximum element because there is no element in the set that is larger than 2, which means its a supernum, and 2 is in the set.

2 is also the supernum of (0,2) but because 2 is not actually in the set, 2 is not the maximum element. Furthermore, for every x in (0,2), there is an x + h that is also in (0,2).

An open interval is distinct from a closed interval in that the end points, in this case 0 and 2, are both limit points of the set, as you can always take an x that is infinitely closer to it than another x, but neither 2 or 0 is actually part of the set. We say that any x in (0,2) is an interior point since there will always be a value less than x and greater than x that is also in (0,2)

>> No.7297233

Just out of interest, how old are you OP?

>> No.7297237

>>7297233
26

I have a CS degree. This graduate level math is fucking me up.

>> No.7297244
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7297244

>>7297038
If you could try to explain exactly where you think this doesn't make sense, that would perhaps make it easier to help you. After years of work in autism aka mathematics, stuff like this is the most obvious thing. But I remember that it didn't use to be like this.

>> No.7297246
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7297246

Hello Josef.

>> No.7297250

>>7297237
>This graduate level math
>Maxima and supermum of sets

This is a joke right?

>> No.7297251

>>7297246
Oh lel.
>old /sci/ will never be back

>> No.7297252

I'm a physics undergrad and I understand this shit just fine. Seriously what do they teach you kids in CS?

>> No.7297656

It's a real number so you can just keep adding more decimals on the open interval. It means that their technically isn't a maximum number less than 2, approaching 2. The closed interval has 2 as the maximum number end of story. I was never educated on what a supremum (I can take a good guess but I'm not giving you my guess) is but I hope this helps you understand it.

>> No.7297664

>>7297140
I'm drunk as hell and I get it. Learned this shit in undergrad analysis.

>> No.7297690

>>7297237
>cs degree

so basically you're an IT guy?

>> No.7297699

>>7297038
The set (0,2) and [0,2] both have a supremum of 2.
The set [0,2] contains 2, so the supremum is the maximum.
The set (0,2) contains all points greater than zeron and less than 2 - so while it is still has 2 as a supremum, there's no max element.
If you think it does, call it X.
X<2 because 2 is not in the set.
Then X + (2 -X) / 2 is an element still in the set but bigger than X. So that contradicts X being the max element.

>> No.7297742

>>7297664
Damn straight.

Remember, supremum is "least upper bound." It is the smallest number that is larger than all the other numbers in the set. So in the open interval, that would be 2. That's different from the maximum number in the set. There is no maximum for open intervals (that's a good exercise for a proof, try one some time.)

>> No.7297755

>>7297656
Supremum is the least upper bound of the set, meaning the minimum of the set of elements greater than any element in the set of which we are taking the supremum.

>> No.7297778

>>7297038
It's false.

by Zorn's lemma, which is equivalent to the axiom of choice, every set has a minimum element.

whoever wrote this doesn't know what they're talking about

>> No.7297781

>>7297742
The supremum doesn't have to be in the set; is this correct? If that is true, how do we know what sort of element the supremum is? Like in this case we are working in script-R but how do you define a supremum for a set of Gaussian Integers?

>> No.7297797

>>7297778
but since it's a set of real numbers, for any arbitrary number in the set, you can find one in between that number and the infimum.

>> No.7297833

>>7297778
jesus, the kind of bullshit you spout daily is amazing. attention whoring + complete bullshit = what the fuck are you doing?

>> No.7297837

>>7297778
(to elaborate, yes you can prove the well-ordering principle with zorn's lemma, but call it that and use it directly. no, that's not what the well-ordering principle means, it means you can create an order in which that applies. we already have an order in R so all you said is useless)

>> No.7297853

>>7297250
>>7297250
Could just be a quick recap in a topology book.

>> No.7297855

>>7297778
retard in zorns lemma the maximal element in the chain doesnt have to necesarily be an element

>> No.7297858

>>7297237
... this is freshman level math. not to put you down or anything, but any introductory mathematics class should have these concepts

>> No.7297868

>>7297237
>This graduate level math
>suprema and maxima

This is undergraduate freshman level math and barely even that.

>I have a CS degree

I am so sorry.

>> No.7297880
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7297880

>>7297237
>I have a CS degree
>but can't comprehend the difference between ≨ and ≤

And yet CS majors will scream from the mountaintops that CS is a subset/superset of pure math

>> No.7297907

>>7297038
OP

If you don't understand the notation,
Given
Open Interval (0,2)
For x being a Real number, not imaginary
then the (0,2) means
0 < x < 2
x < 2; which is x is less than 2
and
x > 0; which means x is greater than 2

Maximum, in mathematical sense requires that it belongs inside the interval (range given)