#
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