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2 gru 2020 · Division is defined by solving an equation that can be easily solved for all pairs x, y of numbers where y ≠ 0. You can give arguments why it is reasonable not to define division by zero, but the fact is that it is not defined. We could easily define division by zero: We could just say that x / y := x whenever y = 0.
Dividing by a really small number makes a really big negative number, so dividing by zero should make negative infinity. 2/0 = ∞ and 2/0 = -∞ can't both be true, so we say 2/0 is undefined instead. There's no definite answer to that equation.
10 sty 2018 · 10 divided by 0 means I am not dividing it, there is 0 division, the number is not being divided. 10 divided by 0 = 10. If you add 0 to any number you have the same original number. If you subtract 0 from any number you have the same original number.
It’s a shorthand for the idea that limit of a/x = 0 is infinity as x goes to 0 (provided that a, x > 0). The idea that limit equals to infinity is again, a bit of a convenient shorthand. Infinity is not a real number and thus you cannot assert its equality to something else.
So for all intents and purposes, no, you cannot* define dividing by 0 as infinity. For example: 1/.01 = 100, 1/.001 = 1,000, 1/.0001 = 10,000, 1/.00001 = 100,000, etc. It's important to understand that limits are not equal to the thing they approach. Take a look at this graph. When x = 3, f(x) = 1.
This resolves your problem because it shows that $\frac{1}{\epsilon}$ will be positive infinity or infinite infinity depending on the sign of the original infinitesimal, while division by zero is still undefined.
6 gru 2021 · The argument follows that as the number approaches zero, the result approaches infinity. Therefore, we should approximate the result for 1/0 as infinity.
