Articles of number systems

Convert numbers from one base to another using repeated divisions.

I have a homework assignment for my programming class to implement an algorithm that can convert from bases 2 trough 16 to any other base from 2 trough 16 but with a few twists. What I need to understand though is how do I convert from a greater base to a lesser one (ex: 16 […]

Fractional number bases

I have a student doing any investigation in to fractional number bases. For example 10 in base (3/2) would be 2101. We can do it manually but to generate enough data to investigate any patterns and other fractional number bases would anybody know how to automate generating the data in Excel, Python or an online […]

Axioms for sets of numbers

What is the most common axiomatic system used by modern mathematicans for the properties of the integers, rationals, reals, and complex numbers? Or does one commonly use a single axiomatic system that is agreed apon, to construct axiomatic systems for the other sets of numbers. Such as using axioms of the integers to construct axioms […]

Essays on the real line?

Are there any essays on real numbers (in general?). Specifically I want to learn more about: The history of (the system of) numbers; their philosophical significance through history; any good essays on their use in physics and the problems of modeling a ‘physical’ line. Cheers. I left this vague as google only supplied Dedekind theory […]

Roman Numbers – Conversion to decimal number

I have read that if a smaller number is to the left of a larger number means that the smaller number has to be subtracted from the larger number. Ok I can understand quickly for below Roman Numbers : IX = X – I = 10 – 1 = 9 But I have difficulty in […]

What is the standardized way to represent $\pi$ in binary notation?

How do I best represent the number $\pi$ in binary? I have been thinking about it for sometime and, if it was me, I would use four bits for each digit, because four bits are sufficient to represent 10-based digits. Something like: 0011 , 0001 0100 0001 … I wouldn’t know, also, how to represent […]

How to find the radix (base) of a number given its representation in another radix (base)?

What’s the method to find the base of any given number? E.g. find $r$ such that $(121)_r=(144)_8$, where $r$ and $8$ are the bases. So how do I find the value of $r$?

Is a non-repeating and non-terminating decimal always an irrational?

We can build $\frac{1}{33}$ like this, $.030303$ $\cdots$ ($03$ repeats). $.0303$ $\cdots$ tends to $\frac{1}{33}$. So,I was wondering this: In the decimal representation, if we start writing the $10$ numerals in such a way that the decimal portion never ends and never repeats; then am I getting closer and closer to some irrational number?

How to prove that every number to the power of any other numbers can be express in a+bi?

I was working on some basic complex numbers and suddenly have a question about it. As you all know, the complex numbers are created as we cannot find a place in the real number system to fit in the value (-1)^(1/2). So we use i to represent it, but how do we know that any […]

Does set $\mathbb{R}^+$ include zero?

I’ve been trying to find answer to this question for some time but in every document I’ve found so far it’s taken for granted that reader know what $\mathbf ℝ^+$ is.