History & Real World Applications

Real World Integers

1. Temperature

We measure temperature in degrees Celsius (°C).

• 0°C: Freezing point of water.
• Positive: Hotter days (e.g., 30°C in Summer).
• Negative: Very cold places (e.g., -10°C in Ladakh).

2. Banking (Debits and Credits)

• Credit (+): Money deposited or added to your account.
• Debit (-): Money spent or taken out.
• If you have ₹100 and spend ₹150, your balance is $100 - 150 = -50$. You owe the bank ₹50.

3. Elevation

• Sea Level: 0 meters.
• Mount Everest: +8848m (Above sea level).
• Mariana Trench: -10,994m (Below sea level).

A Pinch of History

Integers, including zero and negative numbers, have deep roots in India.

• Brahmagupta (628 CE): An Indian mathematician who wrote the Brāhma-sphuṭa-siddhānta. He gave rules for computing with zero and negative numbers long before they were accepted in Europe.

Brahmagupta’s Rules (Simplified)

1. Addition:
   • Sum of two positives is positive.
   • Sum of two negatives is negative.
   • Sum of a positive and negative is the difference between them.
2. Zero:
   • A number plus its inverse is Zero.
   • Subtracting a number from itself is Zero.