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I was reading about Ultrafinitism and the denial of existence of $\lfloor e^{e^{e^{79}}} \rfloor$ by ultrafinitists.

I am wondering if they were to deny the existence of $\lfloor e^{e^{e^{79}}} \rfloor$ shouldn't they actually deny the very existence of $e$ in the first place, let alone forming $e^{e^{e^{79}}}$. Since $e$ in itself is defined/obtained as a limit, if the ultrafinitists were to deny the existence of large numbers then certainly the concept of limit doesn't exist for them. Am I right?

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    That might just be a blunder in representing ultrafinitism's views on Wikipedia's part.2011-08-06
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    What does it mean that a number acutally exists?2011-08-06
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    @Listing: I've always taken the existence of mathematical objects to mean that it's logically possible for states of affairs to exemplify their structure (though not necessarily in our universe). The idea of a "number" though has a lot of distinct meanings attached to it. At any rate, sounds like a philosophical project more than anything else.2011-08-06
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    @Sivaram: Although the limit may not exist, there is certainly a finite-length algorithm for calculating $e$ to arbitrarily high (but finite) precision. So even finitists might believe that $e$ exists, in some suitable sense. I'm not sure about ultrafinitists though.2011-08-06
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    Did you see [this MO-thread](http://mathoverflow.net/questions/44208)? There may be interesting thoughts and pointers to follow (I read it a long time ago, so I may misremember).2011-08-06
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    [A related question](http://math.stackexchange.com/questions/13054).2011-08-07

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