Understanding Bounds in Set Theory, Quizzes of Mathematics

Definitions for the terms 'bounded from above', 'bounded from below', 'bounded', 'upper bound', 'lower bound', 'least upper bound', and 'greatest lower bound' in the context of set theory. It explains what each term means and how they relate to one another.

Typology: Quizzes

2014/2015

Uploaded on 06/23/2015

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TERM 1
Bounded from Above
DEFINITION 1
A set S R is bounded from above if there is a real number M
such that for all xS, xM.
TERM 2
Bounded from Below
DEFINITION 2
A set SR is bounded frombelow if there is a real number M
such that for all xS , Mx.
TERM 3
Bounded
DEFINITION 3
A set is bounded if it is bounded both from above and below.
TERM 4
Upper Bound
DEFINITION 4
If SR a real number M is an upper bound for S if for all xS ,
xM.
TERM 5
Lower Bound
DEFINITION 5
If SR a real number M is alower bound for S if for all xS , Mx.
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TERM 1

Bounded from Above

DEFINITION 1 A set S R is bounded from above if there is a real number M such that for all xS, xM. TERM 2

Bounded from Below

DEFINITION 2 A set SR is bounded frombelow if there is a real number M such that for all xS , Mx. TERM 3

Bounded

DEFINITION 3 A set is bounded if it is bounded both from above and below. TERM 4

Upper Bound

DEFINITION 4 If SR a real number M is an upper bound for S if for all xS , xM. TERM 5

Lower Bound

DEFINITION 5 If SR a real number M is alower bound for S if for all xS , Mx.

TERM 6

Least Upper

Bound

DEFINITION 6 A real number a is a least upper bound for S if a is an upper bound for S with the property that if b is also an upper bound for S then ab. TERM 7

Greatest Lower Bound

DEFINITION 7 A real number a is agreatest lower boundfor S if a is a lower bound for S with the property that if b is any otherlower bound for S then ba.