Comparing integers

Four children are in Bela's Building of Fun.

• Jay is in the Art Centre, on Floor +2.
• Asin is in the Sports Centre, on Floor +5.
• Binnu is in the Cinema Centre, on Floor -3.
• Aman is in the Toy Store, on Floor -1.

Who is on the lowest floor? Binnu, on Floor -3: it is the deepest below the ground.

A lower floor has a smaller number. Floor +3 is lower than Floor +4, so we write +3 < +4 (or +4 > +3). Floor -4 is lower than Floor -3, so -4 < -3 (or -3 > -4). Be careful: 4 is bigger than 3, but -4 is further DOWN than -3, so -4 is the smaller number. In the same way -7 > -25: Floor -7 is far above Floor -25. Of all the negative numbers, -1 is the greatest, the 'king' of the negatives, because it is the highest floor below the ground.

All the negative floors are below Floor 0, so every negative number is less than 0. All the positive floors are above Floor 0, so every positive number is greater than 0. On a number line, smaller numbers lie to the left of bigger ones: 2 < 5, -3 < 2 and -5 < -3.

Integers are the positive numbers, the negative numbers and zero: ... -3, -2, -1, 0, 1, 2, 3 ... (The counting numbers 1, 2, 3, ... are inside this family, and so is 0; fractions like 1/2 are not integers.) The integers between -4 and 4, in increasing order, are -3, -2, -1, 0, 1, 2, 3. 'Between' leaves out -4 and 4 themselves, so there are 7 of them.