OEF Bounds
--- Introduction ---
This module actually contains 6 exercises on the boundedness of
subsets of real numbers: upper bounded, lower bounded, relation with union
and intersection, etc.
Upper bound 1
Let
be a non-empty set. We denote by
its supremum (least upper bound) and
its infimum (greatest lower bound) if they exist. We know that:
.
We can deduce (there can be one or more correct answers):
Upper bound 2
Let
be a non-empty set. We denote by
its supremum (least upper bound) and
its infimum (greatest lower bound) if they exist. We know that:
.
We can deduce (there can be one or more correct answers):
Upper bound 3
Let
and
be two non-empty sets that are bounded . We denote respectively by
and
their bounds. We know that :
.
We can deduce (there can be one or several good answers) :
Borne sup 4
Let
be a non-empty set that is bounded . We denote by
its bound. We know that
.
Choose among the following proposals (only one correct answer)
Image of a function
Let
be function, and let
be a subset of
. Consider the image B=f (A) and the inverse image
of
. What can be said about
and
?
You must choose the most precise replies.
Bounder and union
Let
and
be two subsets of
. Suppose that
(resp.
) is by
(resp. by
). Are the following two statements true?
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- Description: collection of exercises on bounds and boundedness of sets of real numbers. interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: interactive mathematics, interactive math, server side interactivity, analysis, calculus, real_function,bound,upper_bound,image,preimage