31.02 - Ordering of integers

In the previous chapter we talked about integers, let’s expand on that.

When you work with numbers, you want a way to write down which of two numbers is bigger, smaller or equal(or a combination of). The standard way of doing this is trough the symbols:

• $=$ (equal to)
• $!=$ (not equal to)
• $<$ (Less than)
• $\le$ (Less or equal to)
• $>$ (Greater than)
• $\ge$ (Greater or equal to)

Now, for the following examples, let’s visualise a line of integers. We’ll grab a random point in this line, for these examples we’ll use two(2).

Equal to ($=$)

Everything neither on the left or the right of any chosen number is equal to that number. The mathematical way to denote equal to is: $=$.

                             |equal to 2|
... -6, -5, -4, -3, -2, -1, 0, 1,|2|, 3, 4, 5, 6, 7, 8, 9, 10, 11 ...

Some examples of this are:

• $1=1$
• $0=0$
• $-5=-5$

Not equal to ($\ne$)

Everything either on the left or the right of any chosen number is not equal to that number. The mathematical way to denote equal to is: $=$.

                   not equal to 2| |not equal to 2
... -6, -5, -4, -3, -2, -1, 0, 1,|2|, 3, 4, 5, 6, 7, 8, 9, 10, 11 ...

Some examples of this are:

• $1\ne 0$
• $20\ne 5$
• $-5\ne 40$
• $-10\ne -6$

Less than($<$)

Everything to the left of any chosen number is less than that number. The mathematical way to denote less than is: $<$.

                  <-- less than 2| 
... -6, -5, -4, -3, -2, -1, 0, 1,|2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ...

Some examples of this are:

• $1<2$
• $10<50$
• $-5<0$
• $-20<-11$

Less or equal to ($\le$)

Everything to the left but also itself of any chosen number is less or equal to that number. Less or equal to is the same as less than, but it includes the number itself. The mathematical way to denote less or equal to is: $\le$

             <-- less or equal to 2| 
... -6, -5, -4, -3, -2, -1, 0, 1, 2|, 3, 4, 5, 6, 7, 8, 9, 10, 11 ...

Some examples of this are:

• $1\le 2$
• $10\le 10$
• $-6\le 3$
• $-2056\le -2056$

Greater than($>$)

Everything to the right of any chosen number is greater than that number. The mathematical way to denote less than is: $>$.

                                    |greater than 2 -->
... -6, -5, -4, -3, -2, -1, 0, 1, 2,| 3, 4, 5, 6, 7, 8, 9, 10, 11 ...

Some examples of this are:

• $2>1$
• $50>10$
• $5>-6$
• $-11>-20$

Greater or equal to ($\ge$)

Everything to the right but also itself of any chosen number is greater or equal to that number. Greater or equal to is the same as greater than, but it includes the number itself. The mathematical way to denote less or equal to is: $\ge$

                                  |greater or equal to 2 -->
... -6, -5, -4, -3, -2, -1, 0, 1, |2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ...

Some examples of this are:

• $2\ge 1$
• $0\ge -1$
• $10\ge 10$
• $-3\ge -6$
• $2056\ge 2056$

An easy way to remember the symbols

If you look at the symbol $>$, you will notice that the left is wider, bigger, or greater than the right Same with $<$. The left is thinner, smaller, or lesser than the right.

Comparing big numbers

Comparing big numbers may be harder because of their length. A solution would be to:

1. write both numbers below each other:
   $256477,256486$
   

   $256477$
   $256486$
   

2. Compare the top and bottom number, starting on the left. If both numbers are the same, you go one to the right until you find a number that isn’t the same:

   • If all the numbers are the same, both numbers are equal to each other ($=$)
     $\boxed{2564}77$
     $\boxed{2564}86$
     

3. Compare top and bottom to see which of the two is either greater or less (depending on your goal):
   $\boxed{2564}77$
   $\boxed{2564}86$
   $7<8$ Or $8>7$
   

4. Now write the whole numbers again:
   $256477<256486$
   Or
   $256486>256477$

next chapter

The next chapter will go over the sum, difference, product and quotient of numbers