Numbers are small

Numbers Are Just Numbers

Making good choices about retirement involves the processing of numbers. In particular, consumers must have easily available, accurate, and timely numbers, and they must also use them. Contrary to the consumer-driven approach, however, the evidence demonstrates that having an abundance of information does not always translate into it being used to inform choices. The challenge is not merely to ...

Generalized Small Schröder Numbers

We study generalized small Schröder paths in the sense of arbitrary sizes of steps. A generalized small Schröder path is a generalized lattice path from (0, 0) to (2n, 0) with the step set of {(k, k), (l,−l), (2r, 0) | k, l, r ∈ P}, where P is the set of positive integers, which never goes below the x-axis, and with no horizontal steps at level 0. We find a bijection between 5-colored Dyck path...

Small Salem Numbers

Betti numbers are testable ∗

We prove that the Betti numbers of simplicial complexes of bounded vertex degrees are testable in constant time.

What are numbers?

This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality o...