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 […]

An extreme form of constructivism is called finitisim. In this form, unlike the standard axiom system, infinite sets are not allowed. There are important mathematicians, such as Kronecker, who supported such a system. I can see that the natural numbers and rational numbers can easily defined in a finitist system, by easy adaptations of the […]

I was reading the following article on Ultrafinitism, and it mentions that one of the reasons ultrafinitists believe that N is not infinite is because the floor of $e^{e^{e^{79}}}$ is not computable. I was wondering if that’s the case because of technological limitations, or whether there is another reason we cannot find a floor of […]

Suppose you’re trying to teach analysis to a stubborn algebraist who refuses to acknowledge the existence of any characteristic $0$ field other than $\mathbb{Q}$. How ugly are things going to get for him? The algebraist argues that the real numbers are a silly construction because any real number can be approximated to arbitrarily high precision […]

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