# inf (s) and sup (s)

Watch
Announcements

S = {2x^2 : x ∈ R and x^3 > −8}I need help with determining the inf (s) and the sup (s) and whether theyre in the set or not. Thanks in advance.

0

reply

Report

#2

(Original post by

S = {2x^2 : x ∈ R and x^3 > −8}I need help with determining the inf (s) and the sup (s) and whether theyre in the set or not. Thanks in advance.

**omnipotxnce**)S = {2x^2 : x ∈ R and x^3 > −8}I need help with determining the inf (s) and the sup (s) and whether theyre in the set or not. Thanks in advance.

1

reply

(Original post by

It is a good start to determine what are the allowed x values.

**RDKGames**)It is a good start to determine what are the allowed x values.

0

reply

Report

#4

(Original post by

in interval form: S = { (-infinity, +infinity) union [-2,2)} or S = { (-infinity, +infinity) union [-2, +infinity)}

**omnipotxnce**)in interval form: S = { (-infinity, +infinity) union [-2,2)} or S = { (-infinity, +infinity) union [-2, +infinity)}

It's just the solution to x^3 > -8

Also, its INTERSECTION and not UNION.

0

reply

(Original post by

So which one is it?

It's just the solution to x^3 > -8

Also, its INTERSECTION and not UNION.

**RDKGames**)So which one is it?

It's just the solution to x^3 > -8

Also, its INTERSECTION and not UNION.

I struggle so much with real analysis and proof especially so apologies for asking continuous questions.

0

reply

Report

#6

(Original post by

okay so S = { (-infinity,+infinity) intersection [-2,2)} which gives inf (s) = -2, sup (s) doesnt exist and inf (s) is also in the set?

I struggle so much with real analysis and proof especially so apologies for asking continuous questions.

**omnipotxnce**)okay so S = { (-infinity,+infinity) intersection [-2,2)} which gives inf (s) = -2, sup (s) doesnt exist and inf (s) is also in the set?

I struggle so much with real analysis and proof especially so apologies for asking continuous questions.

0

reply

(Original post by

Don't try to work out what S is yet, just work out the set of values s.t. x^3 > -8.

**DFranklin**)Don't try to work out what S is yet, just work out the set of values s.t. x^3 > -8.

0

reply

Report

#8

(Original post by

Im not trying to work out S im trying to work out inf (S) and sup (S) but i dont know how

**omnipotxnce**)Im not trying to work out S im trying to work out inf (S) and sup (S) but i dont know how

You will then need to work out what's actually in S so you can find the sup and inf.

The expressions you've been posting for S are wrong, but because you're trying to do it all at once and not posting working, it's impossible to tell what you're actually doing wrong.

0

reply

(Original post by

The first thing is to work out the set of allowable values for x.

You will then need to work out what's actually in S so you can find the sup and inf.

The expressions you've been posting for S are wrong, but because you're trying to do it all at once and not posting working, it's impossible to tell what you're actually doing wrong.

**DFranklin**)The first thing is to work out the set of allowable values for x.

You will then need to work out what's actually in S so you can find the sup and inf.

The expressions you've been posting for S are wrong, but because you're trying to do it all at once and not posting working, it's impossible to tell what you're actually doing wrong.

0

reply

Report

#10

(Original post by

I literally dont know how to work out what the allowed x values are or how to work out whats actually in S or just how to do the question. My expressions were just in interval form to help me better read them but as youve said im wrong so i have nothing to go off. are u able to show me the steps needs to get the answers i need ?

**omnipotxnce**)I literally dont know how to work out what the allowed x values are or how to work out whats actually in S or just how to do the question. My expressions were just in interval form to help me better read them but as youve said im wrong so i have nothing to go off. are u able to show me the steps needs to get the answers i need ?

0

reply

(Original post by

So, just to be clear: you're telling me you don't know how to find the set of values for which x^3 > -8?

**DFranklin**)So, just to be clear: you're telling me you don't know how to find the set of values for which x^3 > -8?

if this isnt right then yes i dont know how to do it

0

reply

Report

#12

(Original post by

{(-2, + infinity)} ?

if this isnt right then yes i dont know how to do it

**omnipotxnce**){(-2, + infinity)} ?

if this isnt right then yes i dont know how to do it

You can sketch the set of values of S to help you see the inf(S) and to talk about sup(S)

0

reply

Report

#13

**omnipotxnce**)

{(-2, + infinity)} ?

if this isnt right then yes i dont know how to do it

0

reply

(Original post by

As RDK says, that's correct. Follow his advice in post#12

**DFranklin**)As RDK says, that's correct. Follow his advice in post#12

(Original post by

This is correct! So your set S is the equivalent to the values that 2x^2 gives when x is in the set (-2,+inf).

You can sketch the set of values of S to help you see the inf(S) and to talk about sup(S)

**RDKGames**)This is correct! So your set S is the equivalent to the values that 2x^2 gives when x is in the set (-2,+inf).

You can sketch the set of values of S to help you see the inf(S) and to talk about sup(S)

with inf(s) = -2, and sup(s) = 8. inf(s) doesnt exist in the set whereas sup(s) does?

or am i skipping steps again ?

0

reply

Report

#15

(Original post by

okay so would my S then be S = {(8, + infinity) intersection (-2, +infinity)}

with inf(s) = -2, and sup(s) = 8. inf(s) doesnt exist in the set whereas sup(s) does?

or am i skipping steps again ?

**omnipotxnce**)okay so would my S then be S = {(8, + infinity) intersection (-2, +infinity)}

with inf(s) = -2, and sup(s) = 8. inf(s) doesnt exist in the set whereas sup(s) does?

or am i skipping steps again ?

0

reply

Report

#16

**omnipotxnce**)

okay so would my S then be S = {(8, + infinity) intersection (-2, +infinity)}

with inf(s) = -2, and sup(s) = 8. inf(s) doesnt exist in the set whereas sup(s) does?

or am i skipping steps again ?

The set contains the values of for .

Why don't you sketch for ? This is a simple quadratic, The y-values it takes correspond to the set S.

The infimum would be the GREATEST lower bound for the y-values of this quadratic.

0

reply

(Original post by

I think you are having a hard time working with the notation here.

The set contains the values of for .

Why don't you sketch for ? This is a simple quadratic, The y-values it takes correspond to the set S.

The infimum would be the GREATEST lower bound for the y-values of this quadratic.

**RDKGames**)I think you are having a hard time working with the notation here.

The set contains the values of for .

Why don't you sketch for ? This is a simple quadratic, The y-values it takes correspond to the set S.

The infimum would be the GREATEST lower bound for the y-values of this quadratic.

0

reply

Report

#18

(Original post by

so from my sketch i got inf(s) to be 1 and sup (s) is unbounded ?

**omnipotxnce**)so from my sketch i got inf(s) to be 1 and sup (s) is unbounded ?

Check your infimum though. 1 cannot be a lower bound since if x=0.1 then 2x^2 = 0.02 which is less than 1.

0

reply

(Original post by

There is no upper bound, so sup(S) does not exist.

Check your infimum though. 1 cannot be a lower bound since if x=0.1 then 2x^2 = 0.02 which is less than 1.

**RDKGames**)There is no upper bound, so sup(S) does not exist.

Check your infimum though. 1 cannot be a lower bound since if x=0.1 then 2x^2 = 0.02 which is less than 1.

0

reply

Report

#20

(Original post by

so infimum must be 0? as square function corresponds to the postives only so anything below zero becomes positive again

**omnipotxnce**)so infimum must be 0? as square function corresponds to the postives only so anything below zero becomes positive again

0

reply

X

### Quick Reply

Back

to top

to top