# 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?
• I. is by .
• II. is by .
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