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Here, we show you a step-by-step solved example of operations with infinity. This solution was automatically generated by our smart calculator: Apply a property of infinity: $k^ {\infty}=\infty$ if $k>1$. In this case $k$ has the value $2$.
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10 sty 2018 · To put all of this into mathematical terms, dividing by 2 means finding a number (5) by which we can multiply 2 to get 10: 10 / 2 = 5 because 10 = 2 * 5 If we could divide 10 by 0 (I'll call the answer X), we would be saying that: 10 / 0 = X because 10 = 0 * X But zero times anything is 0, so I will never find an X for which this is true.
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.
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.
Division by zero. The reciprocal function y = 1 x. As x approaches zero from the right, y tends to positive infinity. As x approaches zero from the left, y tends to negative infinity. In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.
Sided limits are different here so overall lim x-->0 (1/x) --> undefined or does not exist, but you can see each sided limit has a signed infinity. Compare this to: lim x-->0 (1/x 2) lim x-->0- (1/x 2) = 1/0+ --> +infinity. lim x-->0+ (1/x 2) = 1/0+ --> +infinity.
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.
