# Transfinite arithmetic --- Introduction ---

This is an exercise as well as a game. Let a set $E$ of $k$ elements in the finite ring $ℤ/nℤ$, represented by $k$ integers between 0 and $n-1$. For any element $t\in ℤ/nℤ$, the addition or multiplication by $t$ transforms $E$ into another set ${E}_{t}\subset ℤ/nℤ$.

Thus the exercise generates two sets $E$,$F\subset ℤ/nℤ$, of the same number of elements, and asks you to transform $E$ into $F$ by successive additions and multiplications by elements of $ℤ/nℤ$. And you will be scored according to the number of steps you make.

Severity level:
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9

You can also configure the exercise by a detailed menu .

In order to access WIMS services, you need a browser supporting forms. In order to test the browser you are using, please type the word wims here: and press Enter''.

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

Description: transformation in Z/nZ by addition and multiplication. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, algebra, integers, modular_arithmetic