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It is possible to interpret such expressions in many ways that can make sense. The question is, what properties do we want such an interpretation to have? 0i 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x 0. On the other hand, 0 -1 0 is clearly false (well, almost see the discussion on goblin's answer), and 000 ... This aspect of 0 Day Porn Gem Jewels Amp Rocket Powers Forumporn plays a vital role in practical applications.
Furthermore, inclusion of 0 in the natural numbers is a definition for them that first occurred in the 19th century. The Peano Axioms for natural numbers take 0 to be one though, so if you are working with these axioms (and a lot of natural number theory does) then you take 0 to be a natural number. This aspect of 0 Day Porn Gem Jewels Amp Rocket Powers Forumporn plays a vital role in practical applications.
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Arturo I heartily disagree with your first sentence. Here's why There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer). For all this, 001 is extremely convenient, and I wouldn't know how to do without it. In my lectures, I always tell my students that whatever their teachers said in school about 00 being undefined, we ... This aspect of 0 Day Porn Gem Jewels Amp Rocket Powers Forumporn plays a vital role in practical applications.
Furthermore, your title says something else than "infinity times zero". It says "infinity to the zeroth power". It is also an indefinite form because infty0 exp (0log infty) but loginftyinfty, so the argument of the exponential is the indeterminate form "zero times infinity" discussed at the beginning. This aspect of 0 Day Porn Gem Jewels Amp Rocket Powers Forumporn plays a vital role in practical applications.
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Furthermore, what is 0 i? - Mathematics Stack Exchange. This aspect of 0 Day Porn Gem Jewels Amp Rocket Powers Forumporn plays a vital role in practical applications.
Moreover, your title says something else than "infinity times zero". It says "infinity to the zeroth power". It is also an indefinite form because infty0 exp (0log infty) but loginftyinfty, so the argument of the exponential is the indeterminate form "zero times infinity" discussed at the beginning. This aspect of 0 Day Porn Gem Jewels Amp Rocket Powers Forumporn plays a vital role in practical applications.
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