# Tagged Questions

Questions on the different ways to represent a number, how to convert between those different ways, and other such questions. The usual system employed by humans is the decimal (base-10) system, but other systems like binary and hexadecimal are also in frequent use.

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### Is there a third dimension of numbers?

Is there a third dimension of numbers like real numbers, imaginary numbers, [blank] numbers?
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### What could be better than base 10?

Most people use base 10; it's obviously the common notation in the modern world. However, if we could change what became the common notation, would there be a better choice? I'm aware that it very ...
3k views

### why have we chosen our number system to be decimal (base 10)

After learning about the binary number system (only 2 symbols, i.e. 0 and 1), I just thought why did we adopt the decimal number system (10 symbols) after all? I mean if you go to see, it's rather ...
516 views

### Why is 8 so special?

I have been reading about multi-dimensional numbers, and found out that it's been proven that Octonions are the division algebra of the largest dimension. I was wondering why despite having infinitely ...
166 views

### Uniqueness of the infinite expansion in base $b$

If $b>1$ is an integer, is well know that the numbers $x\in (0,1]$, can be written as $$x = \sum_{k=1}^{\infty} \frac{a_k}{b^k}$$ for some integers $a_k \in \{0,1,\ldots ,b-1\}$. When ...
666 views

### The largest number system

If my number set construction memory doesn't fail me (I'll edit if errors are pointed out), we start out with Peano's axioms to get to $\mathbb{N}$, and in the need of an additive inverse for its ...
10k views

### Is '10' a magical number or I am missing something?

It's a hilarious witty joke that points out how every base is '10' in its base. Like, 2 = 10 (base 2) 8 = 10 (base 8) My question is if whoever invented the ...
604 views

### What's the hard part of zero?

A lot of textbooks said it was hard for human to accept zero when it was first introduced. How could it be? It seems to me as natural as positive integer which represent there is no elements at all.
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### Converting decimal(base 10) numbers to binary by repeatedly dividing by 2

A friend of mine had a homework assignment where he needed to convert decimal(base 10) numbers to binary. I helped him out and explained one of the ways I was taught to do this. The way I showed him ...
110 views

### 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 ...
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### Finding a bijective function from integer to words

I need to find a function to enumerate the ordered list of sequential words based on a charset. Let me give you an example. If the charset is "abc", the function to be found "f" should compute the ...