But in likelihood, which is clearly not the case, since we are using a weighted normal of probable outcomes, and also the weighted common alone could possibly be an unlikely, or simply difficult result. For example, whenever you roll a die, you "assume" the worth with the number revealed for being 3.five, Though you realize that won't ever happen. Equally, we can "anticipate" the outcome of an experiment to become infinite, Despite the fact that We all know it will be finite. That explanation won't thoroughly satisfy your instinct, but it's a get started at the least. Share Cite
(two) in an enriched range system containing the two infinite quantities and infinitesimals, including the hyperreals, you can avoid discussing things such as indeterminate varieties
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not all wrongnot all Completely wrong sixteen.4k22 gold badges3737 silver badges5757 bronze badges $endgroup$ Include a comment
– user14972 Commented Jan twenty five, 2014 at 12:forty eight $begingroup$ Not likely.. I remaining it for the reader no matter whether he hopes to think that, or just consider the definition to become a description of what is infinite. Certainly there might be many things that "have more substantial magnitude than any finite variety", and double any these kinds of matter also satisfies Infinite Craft the exact same assets.
I'm undecided if you will discover other approaches to prove it. Perhaps There exists a way with what are generally known as Fourier series, as a lot of collection could be stumbled upon in this way, but it's not that instructive. $endgroup$
Obviously $alpha$ is infinite if and only if $alpha$ is transfinite. But Take note that it's according to The truth that $leq$ is trichotomous, i.e., for almost any ordinals $alpha,beta$ possibly $alphaleqbeta$ or $betaleqalpha$.
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