In mathematics, 1 divided by 0 is undefined or impossible to calculate.
Why Division by Zero is Undefined
As stated by Sal Khan, while we would like to have an answer for "what's 1 divided by 0?", it's simply not possible. The fundamental issue lies in the definition of division itself. Division is the inverse operation of multiplication. This means if we say 'a / b = c', then it should also mean that 'b * c = a'.
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Applying this to our problem: If we were to say that 1 / 0 = x, it would imply that 0 * x = 1.
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The contradiction: However, any number multiplied by zero is always zero. Therefore, there is no number 'x' that can satisfy the equation 0 * x = 1. This is because zero times anything equals zero, never one.
Exploring the Concept
Let's examine this using a table:
| Division Problem | Result (Hypothetical) | Multiplication Check | Validity |
|---|---|---|---|
| 6 / 3 = 2 | 2 | 3 * 2 = 6 | Valid |
| 10 / 2 = 5 | 5 | 2 * 5 = 10 | Valid |
| 1 / 0 = ? | Hypothetical Value | 0 Hypothetical Value* = 1 | Invalid |
- The table demonstrates how division works in normal cases, where the result can be verified by multiplication.
- However, the multiplication check fails when we try to divide by zero, because the multiplication result is always zero.
What Happens in Practice
Because of the lack of a valid result, division by zero leads to issues in various contexts:
- Calculators and Computers: Most calculators and computer programs return an error when encountering a division by zero. This error often indicates that the operation is "undefined."
- Mathematical Proofs: Division by zero can also cause invalid results in mathematical proofs.
Conclusion
Trying to divide any number by zero breaks the fundamental laws of mathematics. There is simply no value that can satisfy the requirement that multiplying the denominator (0) by the result equals the numerator (1). Therefore, 1 divided by 0 is considered undefined.
