Integers

Transcript

Integers Brahmagupta asked a simple question: what happens if you subtract a larger number from a smaller one, like 3 - 5? To answer this, he looked at commerce and trade, realizing that numbers could represent both having something and owing something. THE UNANSWERED QUESTION: VISUALIZING THE PROBLEM 5 Coins -5 Coins 3 Coins - 5 Coins = [?]Fortunes and Debts He introduced two states. Fortunes (Dhana) are positive numbers representing wealth. Debts (Rina) are negative numbers representing what is owed. BRAHMAGUPTA'S REAL-WORLD SOLUTION: DHANA & RIN़A HE INTEGER NUMBER LINE: THE BIRTH OF NEGATIVE NUMBER Negative Integers ⟵ Debt (Rina) Fortunes (Dhana) → Positive IntegersBRAHMAGUPTA'S REAL-WORLD SOLUTION: DHANA \& RIN़A HE INTEGER NUMBER LINE: THE BIRTH OF NEGATIVE NUMBER Negative Integers ⟵ Debt (Rina) Fortunes (Dhana) → Positive IntegersBRAHMAGUPTA'S REAL-WORLD SOLUTION: DHANA \& RIN़A HE INTEGER NUMBER LINE: THE BIRTH OF NEGATIVE NUMBER Negative Integers ⟵ Debt (Rina) Fortunes (Dhana) → Positive IntegersTogether, positive natural numbers, their negative counterparts, and zero create the set of Integers (denoted by the symbol 𝒁)