# OEF finite map --- Introduction ---

This module actually contains 12 exercises on maps between finite sets represented by integers. The main goal of these exercises is to acquire the notions of surjectivity, injectivity, bijectivity, image, inverse image, etc.

### Bijectivity by polynomial

Consider the map {0,1,...,} defined by

(mod ).

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Image by polynomial

Consider the map {0,1,...,} defined by

(mod ).

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Elements by polynomial

Consider the map {0,1,...,} defined by

(mod ).

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Inverse image by polynomial

Consider the map {0,1,...,} defined by

(mod ).

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Table by polynomial

Consider the map {0,1,...,} defined by the following polynomial. Determine this map by filling in the table bellow.

(mod ).

### Bijectivity by table

Consider the map {0,1,...,} defined by

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Cube by table

Consider the map {0,1,...,} defined by the following table. Fill-in the last line of the table.

### Image by table

Consider the map {0,1,...,} defined by

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Inverse map by table

Consider the map {0,1,...,} defined by the following table. Fill-in the last line of the table.

### Elements by table

Consider the map {0,1,...,} defined by

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Inverse image by table

Consider the map {0,1,...,} defined by

What is the nature of ?
What is the cardinal of the image of ?
Give an element having several inverse images.
Give an element having several images.
Give an element without inverse image.
Give an element without image.
What is the image of ?
What is the inverse image of the subset {}?

Help. Enter -1 if the asked elements do not exist.

### Square by table

Consider the map {0,1,...,} defined by the following table. Fill-in the last line of the table.

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