The line carries on
How Can a Number Be Less Than Nothing?
Negative numbers are what you get when the number line keeps going past zero.
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Step 1 of 5
Counting down does not have to stop at zero.
Three, two, one, zero — and there is no reason to halt. The pattern of stepping one to the left works perfectly well past that point.
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Step 2 of 5
A negative says which side of zero you are on.
The minus sign is a direction, not a flaw. It says this number sits to the left of zero, exactly as far as its size suggests.
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Step 3 of 5
They describe real things, not just puzzles.
A temperature below freezing, a floor below ground, a bank balance you owe. All are quantities that genuinely run past zero.
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Step 4 of 5
Adding a negative is the same as taking away.
Moving five to the left is what subtracting five has always meant, so adding negative five and subtracting five do exactly the same job.
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Step 5 of 5
Two negatives cancel out.
Taking away a debt leaves you better off, so subtracting a negative moves you right. That is why two minus signs make a plus.
Negative numbers were rejected as absurd by European mathematicians into the 1700s, long after Indian and Chinese texts used them freely.
The short version
Negative numbers are simply the number line continuing past zero, and the minus sign tells you which side of zero a number sits on.
Try it yourself
Look at a lift's button panel in a building with a basement. The floors below ground are negative numbers doing an everyday job.
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