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1.1A — Integers & Whole Numbers

Now pause for a second and think about the jumping jacks you just did.

When you counted your jumping jacks, you used numbers like 1, 2, 3, 4, 5, and maybe even higher. These numbers are called whole numbers because they are complete counting numbers. Whole numbers help us count real actions, real movements, and real things we can actually measure.

If you completed 6 jumping jacks, your brain automatically used a whole number because you counted something real. If you completed 15 jumping jacks, that is still a whole number. Every jump, every clap, every movement could be counted clearly.

But now imagine someone saying, “I just finished -10 jumping jacks.” Wait a second… forget how that sounds, what would that even look like? Would they jump backwards into the past? Would the jumping jacks magically disappear? Sounds strange, right? That is because some numbers behave differently from others. Whole numbers begin at 0 and continue forever, like, 0, 1, 2, 3, 4, 5, and so on. Notice something important here, Zero is included. Before you started your warm-up, how many jumping jacks had you completed? Zero. You had not started moving yet, but zero still represented a real amount. That is why zero is a whole number.

Now let’s step into a bigger number world: integers. Integers are like a larger number family. They include all the whole numbers you already know, numbers like 0, 1, 2, 3, 4, 5…

But integers also include numbers below zero, like -1, -2, -3, and more. This means integers can move in two directions — above zero and below zero.

Now think carefully about your warm-up again. Could you complete 8 jumping jacks? Of course. Could you complete 15 jumping jacks? You could. But could you complete -8 jumping jacks? No. A negative jumping jack does not physically exist. You cannot jump “less than nothing.” And this is where the difference between whole numbers and integers becomes much clearer.

Whole numbers are numbers we use to count the jumping jacks you actually completed.

Integers are a bigger group because they include negative numbers too, even if those negative numbers cannot always represent physical actions during the warm-up.

And that leads us to one very important mathematical idea; Every whole number is an integer, but not every integer is a whole number. In plain words; five is both a whole number and an integer; zero is both a whole number and an integer, but -5 is only an integer.