# Special Numbers: update

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This post is a continuation of my earlier post: Special Numbers

Four (4)

This is the only euclidean space with properties different from other n-dimensional euclidean spaces. For example, there are smooth 4-manifolds which are homeomorphic but not diffeomorphic.  Put differently, for any dimension except four there is only one differentiable structure on the space underlying the Euclidean space of that dimension. For a discussion in this direction see this article by Liviu Nicolaescu. For other special properties of 4-dimesnions read Wikipedia article on 4-manifold.
Thanks to Dr. Ritwik Mukherjee for explaining this fact about four-space.

# Special Numbers

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Recently I realized the special properties of following numbers:

Zero (0)

It is the only number which is both real and purely imaginary at same time.

One (1)

It is sufficient to create all the counting numbers (a.k.a. natural numbers).

Two (2)

This is the maximum exponent, $n$, for which $x^n + y^n=z^n$ has solution in natural numbers. This peculiar property leads to “Fermat’s Last Theorem”.

If you also have some special numbers in mind, please do share them below as comments.