Is 0 0 Infinity

This may be easier to see if you rewrite to lim_xtoinfty fxfrac1hx where lim_xtoinfty fx 0 and lim_xtoinfty frac1hx0 and the product of two functions that both have limit 0 surely also has limit 0. Frac0infty is not an indeterminate form.

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If 0 0 infty times 0 neq 0 0 0 then 0 0 0neq 0 0 0.

Is 0 0 infinity. On the contrary those limits tell you that the limit of the entire quotient is 0. So in answer to your question. See common false rebuttals.

You are correct but infinity is not a number. 0 0 is neither zero nor infinity but can take any value including zero or plus or minus infinity if it arises in the form of some. And hence it does not apply to infinity.

But any number multiplied with zero is zero why is this not the case here.

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