Are sup, inf, max, min correct for the set ${frac{x}{x+1}: x in A}$?
Let $A subseteq (0, +infty)$ be such that $inf A=0$ and $A$ is NOT bounded from above. Find, if they exist, max, min, sup, inf of the set
$$B=bigg{ frac{x}{x+1}: x in A bigg}.$$
I think that
$$sup B = 1, spaceinf B = 0,space nexists max B,space nexists min B$$
but I am not sure if it is right. Could you help me?
real-analysis supremum-and-infimum
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
asked Feb 10 '14 at 23:39
evinda
4,04531750
add a comment |
Let $A subseteq (0, +infty)$ be such that $inf A=0$ and $A$ is NOT bounded from above. Find, if they exist, max, min, sup, inf of the set
$$B=bigg{ frac{x}{x+1}: x in A bigg}.$$
I think that
$$sup B = 1, spaceinf B = 0,space nexists max B,space nexists min B$$
but I am not sure if it is right. Could you help me?
real-analysis supremum-and-infimum
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
asked Feb 10 '14 at 23:39
evinda
4,04531750
1
What would happen if $A={2,1,frac12,frac14, frac18,ldots}$? Or if $A$ is the open interval $(0,2)$?
– Henry
Feb 10 '14 at 23:42
@Henry I got stuck now!!Could you give me a hint??
– evinda
Feb 10 '14 at 23:47
@Henry I just edited my post!!!A is NOT bounded from above!!!!
– evinda
Feb 10 '14 at 23:55
evinda: so try $A={ldots ,8,4,2,1,frac12,frac14, frac18,ldots}$ i.e. all powers of $2$, or $A = (0, +infty)$
– Henry
Feb 11 '14 at 0:45
add a comment |
Let $A subseteq (0, +infty)$ be such that $inf A=0$ and $A$ is NOT bounded from above. Find, if they exist, max, min, sup, inf of the set
$$B=bigg{ frac{x}{x+1}: x in A bigg}.$$
I think that
$$sup B = 1, spaceinf B = 0,space nexists max B,space nexists min B$$
but I am not sure if it is right. Could you help me?
real-analysis supremum-and-infimum
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
asked Feb 10 '14 at 23:39
evinda
4,04531750
Let $A subseteq (0, +infty)$ be such that $inf A=0$ and $A$ is NOT bounded from above. Find, if they exist, max, min, sup, inf of the set
$$B=bigg{ frac{x}{x+1}: x in A bigg}.$$
I think that
$$sup B = 1, spaceinf B = 0,space nexists max B,space nexists min B$$
but I am not sure if it is right. Could you help me?
real-analysis supremum-and-infimum
real-analysis supremum-and-infimum
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
asked Feb 10 '14 at 23:39
evinda
4,04531750
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
asked Feb 10 '14 at 23:39
evinda
4,04531750
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
edited Dec 9 at 9:52
Martin Sleziak
44.7k7115270
44.7k7115270
asked Feb 10 '14 at 23:39
evinda
4,04531750
asked Feb 10 '14 at 23:39
evinda
4,04531750
asked Feb 10 '14 at 23:39
evinda
4,04531750
4,04531750
1
What would happen if $A={2,1,frac12,frac14, frac18,ldots}$? Or if $A$ is the open interval $(0,2)$?
– Henry
Feb 10 '14 at 23:42
@Henry I got stuck now!!Could you give me a hint??
– evinda
Feb 10 '14 at 23:47
@Henry I just edited my post!!!A is NOT bounded from above!!!!
– evinda
Feb 10 '14 at 23:55
evinda: so try $A={ldots ,8,4,2,1,frac12,frac14, frac18,ldots}$ i.e. all powers of $2$, or $A = (0, +infty)$
– Henry
Feb 11 '14 at 0:45
add a comment |
1
What would happen if $A={2,1,frac12,frac14, frac18,ldots}$? Or if $A$ is the open interval $(0,2)$?
– Henry
Feb 10 '14 at 23:42
@Henry I got stuck now!!Could you give me a hint??
– evinda
Feb 10 '14 at 23:47
@Henry I just edited my post!!!A is NOT bounded from above!!!!
– evinda
Feb 10 '14 at 23:55
evinda: so try $A={ldots ,8,4,2,1,frac12,frac14, frac18,ldots}$ i.e. all powers of $2$, or $A = (0, +infty)$
– Henry
Feb 11 '14 at 0:45
1
1
What would happen if $A={2,1,frac12,frac14, frac18,ldots}$? Or if $A$ is the open interval $(0,2)$?
– Henry
Feb 10 '14 at 23:42
What would happen if $A={2,1,frac12,frac14, frac18,ldots}$? Or if $A$ is the open interval $(0,2)$?
– Henry
Feb 10 '14 at 23:42
@Henry I got stuck now!!Could you give me a hint??
– evinda
Feb 10 '14 at 23:47
@Henry I got stuck now!!Could you give me a hint??
– evinda
Feb 10 '14 at 23:47
@Henry I just edited my post!!!A is NOT bounded from above!!!!
– evinda
Feb 10 '14 at 23:55
@Henry I just edited my post!!!A is NOT bounded from above!!!!
– evinda
Feb 10 '14 at 23:55
evinda: so try $A={ldots ,8,4,2,1,frac12,frac14, frac18,ldots}$ i.e. all powers of $2$, or $A = (0, +infty)$
– Henry
Feb 11 '14 at 0:45
evinda: so try $A={ldots ,8,4,2,1,frac12,frac14, frac18,ldots}$ i.e. all powers of $2$, or $A = (0, +infty)$
– Henry
Feb 11 '14 at 0:45
add a comment |
1 Answer
1
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votes
With your edit (the word NOT), your suggested answers look correct.
Clearly $0 lt frac{x}{x+1} lt 1$ if $x$ is positive, and it approaches but does not achieve $0$ for very small $x$, and approaches but does not achieve $1$ for very large $x$
answered Feb 11 '14 at 0:49
Henry
98.1k475161
Great!!!Thank you very much!!!
– evinda
Feb 11 '14 at 0:57
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
With your edit (the word NOT), your suggested answers look correct.
Clearly $0 lt frac{x}{x+1} lt 1$ if $x$ is positive, and it approaches but does not achieve $0$ for very small $x$, and approaches but does not achieve $1$ for very large $x$
answered Feb 11 '14 at 0:49
Henry
98.1k475161
Great!!!Thank you very much!!!
– evinda
Feb 11 '14 at 0:57
add a comment |
With your edit (the word NOT), your suggested answers look correct.
Clearly $0 lt frac{x}{x+1} lt 1$ if $x$ is positive, and it approaches but does not achieve $0$ for very small $x$, and approaches but does not achieve $1$ for very large $x$
answered Feb 11 '14 at 0:49
Henry
98.1k475161
Great!!!Thank you very much!!!
– evinda
Feb 11 '14 at 0:57
add a comment |
With your edit (the word NOT), your suggested answers look correct.
Clearly $0 lt frac{x}{x+1} lt 1$ if $x$ is positive, and it approaches but does not achieve $0$ for very small $x$, and approaches but does not achieve $1$ for very large $x$
answered Feb 11 '14 at 0:49
Henry
98.1k475161
With your edit (the word NOT), your suggested answers look correct.
Clearly $0 lt frac{x}{x+1} lt 1$ if $x$ is positive, and it approaches but does not achieve $0$ for very small $x$, and approaches but does not achieve $1$ for very large $x$
answered Feb 11 '14 at 0:49
Henry
98.1k475161
answered Feb 11 '14 at 0:49
Henry
98.1k475161
answered Feb 11 '14 at 0:49
Henry
98.1k475161
answered Feb 11 '14 at 0:49
Henry
98.1k475161
98.1k475161
Great!!!Thank you very much!!!
– evinda
Feb 11 '14 at 0:57
add a comment |
Great!!!Thank you very much!!!
– evinda
Feb 11 '14 at 0:57
Great!!!Thank you very much!!!
– evinda
Feb 11 '14 at 0:57
Great!!!Thank you very much!!!
– evinda
Feb 11 '14 at 0:57
add a comment |
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1
What would happen if $A={2,1,frac12,frac14, frac18,ldots}$? Or if $A$ is the open interval $(0,2)$?
– Henry
Feb 10 '14 at 23:42
@Henry I got stuck now!!Could you give me a hint??
– evinda
Feb 10 '14 at 23:47
@Henry I just edited my post!!!A is NOT bounded from above!!!!
– evinda
Feb 10 '14 at 23:55
evinda: so try $A={ldots ,8,4,2,1,frac12,frac14, frac18,ldots}$ i.e. all powers of $2$, or $A = (0, +infty)$
– Henry
Feb 11 '14 at 0:45