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.
27
votes
7answers
2k views
Is there a third dimension of numbers?
Is there a third dimension of numbers like real numbers, imaginary numbers, [blank] numbers?
22
votes
9answers
721 views
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 ...
15
votes
6answers
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 ...
9
votes
1answer
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 ...
3
votes
1answer
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 ...
7
votes
3answers
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 ...
151
votes
10answers
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 ...
10
votes
7answers
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.
8
votes
2answers
447 views
Surreal and ordinal numbers
Is there a surjective map between the (class of) ordinal numbers On and the set No (Conway's surreal numbers) and is it constructable, In Conway's system we have for example:
$\omega_0 = < ...
11
votes
2answers
309 views
Are surreal numbers actually well-defined in ZFC?
Thinking about surreal numbers, I've now got doubts that they are actually well-defined in ZFC. Here's my reasoning:
The first thing to notice is that the surreal numbers (assuming they are well ...
8
votes
1answer
424 views
Surreal numbers without the axiom of infinity
Let $ZF^\times$ denote the set of axioms of Zermelo-Fraenkel set theory without the axiom of infinity. The set $V_\omega$ of all hereditarily finite sets is a model of $ZF^\times$, and ...
3
votes
3answers
292 views
Is it true that all senary numbers ending in 1 and 5 are primes?
I was reading the Wikipedia article on senary numbers (base 6), which states that:
all primes, when expressed in
base-six, other than 2 and 3 have 1 or
5 as the final digit
Unless I am ...
1
vote
2answers
85 views
General approach for problem for finding sum from $1$ to $N$ when all $a$'s are replaced by $b$'s
The problem is:
Find the sum of all the numbers from $1$ to $100$ when all the $6$'s are replaced by $9$'s.
I need some ideas on how to approach this kind of problems? Please explain your ideas, ...
9
votes
3answers
293 views
Advocating base 12 number system
I had a calculus professor who suggested we should be using base 12 number system. What are the advantages of using such a system?
6
votes
2answers
818 views
In a Venn diagram, where are other number sets located?
I remember of this image I've learned at school:
I've heard about other number (which I'm not really sure if they belong to a new set) such as quaternions, p-adic numbers. Then I got three ...
3
votes
2answers
286 views
Is there is a number system which is extension of complex number system?
Complex number system is extension of real number system. Is there is a number system which is extension of complex number system in which algebra is well defined?
11
votes
5answers
461 views
How do you say $10$ when it's in binary?
I always assumed $10$ was pronounced "ten" regardless of whether it's binary, decimal, or another system, just like how 5 is "five" in all systems that the digit exists exists. But someone told me ...
5
votes
4answers
785 views
what base number system is the hebrew language?
In the hebrew bible, there number system is based off of hebrew letters. There is a single digit used going all the way up to 10, then it uses two digits... Untill it gets to 20, which is a single ...
3
votes
1answer
264 views
What's the difference between hyperreal and surreal numbers?
The Wikipedia article on surreal numbers states that hyperreal numbers are a subfield of the surreals. If I understand correctly, both fields contain:
real numbers
a hierarchy of infinitesimal ...
2
votes
0answers
148 views
What is the origin of the (nearly obsolete) term “binary decimal”?
What is the origin of the (nearly obsolete) term "binary decimal"?
At least two important publications in the 1930s used this oxymoron to mean what is now ...
5
votes
3answers
991 views
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 ...
4
votes
2answers
641 views
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 ...
2
votes
2answers
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 ...
2
votes
2answers
214 views
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 ...
1
vote
4answers
2k views
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 ...
0
votes
1answer
63 views
