The set of integers
Operations with integers I
 
1. Sets of numbers

Natural numbers. The set N.

The concept of number is understood as the expression of a value, the quantification of a magnitude.
Natural numbers express values regarding whole -not divided- things. Natural numbers are counted one by one starting with 0. They don't allow the partition of units and they only express positive values.

N={0, 1, 2, 3, 4, 5, 6, ... ... ...}

But how can we express  height, depth, wealth, debts, profits, economic loss, temperature in numbers?
Integers

Sometimes we need to express values that are below the value considered as a starting point or value zero.
For that reason, we need to enlarge the set of numbers including the negative ones, too. In order to do this, we add a sign + or - to the natural number.
Integers have arisen from this idea: they express values one by one, but they can express positive values and negative values, as well.
Writing of an integer. The set Z.

There are two parts in the written expression of an integer: the sign and the absolute value.
The set of integers is called with the letter Z.

Z={... ... ... -7, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, ... ... ...}

The set of integers is infinite both in negative and in positive direction.
The natural numbers are part of the set of integers, they are the positive integers.
It is a good idea to look for the easiest way to express a number. Therefore, when writing a positive integer, it is better not to write down the + sign, but instead, leave it as a natural number.
There are other wider sets of numbers.
Probably you also know decimal and rational numbers. But there are also other numbers you will study for the next academic years. They appeared to express values that couldn't be written using the numbers known until then. The wider sets of numbers include the previous sets inside them.
2. Graphical representation of integers.

Integers are represented by means of dots on a straight line, but before that, we must set the position of dot 0 and the length of the segment unit, which will be placed on the line consecutively depending on the value of the number. Positive numbers are placed on the right and negative numbers on the left.
If it is a vertical line, positive numbers are placed above and negative numbers below.

Put the following dots on the line.
Esta unidad interactiva requiere la máquina virtual de Java J2RE.

3. Ordering of integers.

Esta unidad interactiva requiere la máquina virtual de Java J2RE. 		Drag the numbers into the right order, from lowest to highest.
         
           
  Eduardo Barbero Corral
 
Spanish Ministry of Education. Year 2007
 
 


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