Fortunes and debts

The idea

Negative numbers lie to the left of zero on the number line; the positive natural numbers, their negatives and zero together form the set of integers, ℤ.

Paying more than you have

Brahmagupta asked: 5 − 5 = 0, but what about 3 − 5? You cannot take 5 apples from 3 apples. But you can owe someone ₹2.

You have ₹3 and must pay ₹5. Where do you think the answer is on the number line?

• At 0
• To the left of 0
• To the right of 5

Walk the line

Right of 0 is a fortune (dhana). Left of 0 is a debt (ṛiṇa). Walk the marker.

Left of zero

Negative numbers lie to the left of zero on the number line. The positive natural numbers, their negatives and zero together form the integers, written ℤ.

Brahmagupta called positive numbers fortunes (dhana) and negative numbers debts (ṛiṇa). The symbol ℤ comes from the German word *Zahlen*, which means numbers.

Notes

Integers ℤ: negative numbers (left of 0), zero and the positive natural numbers.

Check yourself

Where does −4 lie on the number line?

You have ₹3 and pay ₹5. What is 3 − 5?

Which of these is an integer?

Which numbers together form the integers ℤ?

• To the left of 0 — correct. Yes. Negative numbers lie to the left of 0.
• To the right of 0. The right side holds the positive numbers (fortunes).
• At 0. 0 is neither a fortune nor a debt. −4 is a debt.
• −8. You do not add the amounts. 5 − 3 = 2 is how far you are below 0.
• −2 — correct. Yes. You are ₹2 in debt, which is −2.
• 2. You still owe money, so the answer is a debt. That makes it negative.
• −7 — correct. Yes. −7 is the negative of the natural number 7.
• 0.5. 0.5 lies between 0 and 1. It is not an integer.
• 3/4. A fraction like 3/4 lies between 0 and 1. It is not an integer.
• Only the positive numbers. The integers also include zero and the negatives.
• The positive natural numbers, their negatives and zero — correct. Yes. That is {…, −2, −1, 0, 1, 2, …}.
• Only the negative numbers. The integers also include zero and the positive numbers.