It is undefined.
In infinities and infinitessimals we use limits, so we see trends as we approach a limit. However this gives different answers, The limit as A approaches infinity of A x 0 is 0. But the limit as B approaches zero of infinty x B is infinite. To be well-defined both of these answers need to be the same.
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No. Zero multiplied or divided by anything is zero.
Infinity divided by any finite number is infinity. Here are the rules: 1. Infinity divided by a finite number is infinite (I / f = I); 2. Any finite number divided by infinity is a number infinitesimally larger than, but never equal to, zero (f / I = 1 / I); 3. Infinity divided by infinity is one (I / I = 1), or in fact any other positive number (I / I = and so on...); 4. Infinity multiplied by zero (no infinity) is zero (I * 0 = 0); 5. Infinity divided by a positive finite number is infinity (I / +f = I); 6. Infinity divided by a negative finite number is minus infinity (I / -f = -I); 7. Infinity divided by zero is not possible; 8. Infinity plus infinity is infinity (I + I = I); 9. Zero divided by infinity (nothing divided into infinity) equals zero (0 / I = 0); 10. Infinity plus a finite number is infinity (I + f = I); 11. Infinity minus a finite number is infinity (I - f = I); but 12. Infinity minus infinity, due to the nature of infinity, can be zero, infinity, or minus infinity (I - I = -I, 0, I).
Infinity
Infinity cannot, by definition, be a defined number such as zero.
that would be 2 times infinity.