Linked Questions

0
votes
1answer
613 views

Why 1 is not prime [duplicate]

I have been told that there is some interesting mathematics to why the number 1 is not prime. Can someone explain why one is not a prime number?
0
votes
2answers
285 views

Why $1$ isn't a prime? [duplicate]

I was wondering the reason behind defining the Prime Numbers in a manner of which $1$ isn't an example. I read in Rotman's A First Course in Abstract Algebra that one reason that $1$ is not called a ...
5
votes
4answers
161 views

Should we or should we not take $1$ as a prime number? [duplicate]

I think I know that there were times in the past when it was convenient to look at a number $1$ as a prime number, and, as far as I can remember, even then it was dependent on who we ask is it prime ...
-1
votes
2answers
89 views

What will accepting 1 as prime change? [duplicate]

How significant is the fact 1 isn't a prime number? What will happen if it is? What areas of Mathematics are affected by changing the fact? I know why and how 1 isn't a prime. My question is how ...
0
votes
1answer
140 views

Why was 1 considered as prime years ago? [duplicate]

I've seen on Maths Is Fun that years ago, 1 was considered as prime, but now, it is not. How did this happen? I know that a prime number has only two factors, 1 and itself, and we have 1, which is ...
0
votes
0answers
55 views

Prime - number theory [duplicate]

Why is the digit 1 is not a prime number? 1 can be devided by 1 and itself. I think it's because we can express like 1= 1x1x1 ... is it true or not?
38
votes
14answers
4k views

Is the number $-1$ prime?

From my understanding it's not prime because it's not greater than $0$. So my followup question is why did mathematicians exclude $-1$? The definition of prime is having only two factors. $-1 \cdot ...
32
votes
9answers
4k views

Why is $x^0 = 1$ except when $x = 0$?

Why is any number (other than zero) to the power of zero equal to one? Please include in your answer an explanation of why $0^0$ should be undefined.
40
votes
2answers
14k views

Characterizing units in polynomial rings

I am trying to prove a result, for which I have got one part, but I am not able to get the converse part. Theorem. Let $R$ be a commutative ring with $1$. Then $f(X)=a_{0}+a_{1}X+a_{2}X^{2} + \cdots +...
37
votes
3answers
6k views

Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?

I know that $1$ is not a prime number because $1\cdot\mathbb Z=\mathbb Z$ is, by convention, not a prime ideal in the ring $\mathbb Z$. However, since $\mathbb Z$ is a domain, $0\cdot\mathbb Z=0$ is ...
4
votes
5answers
4k views

Why is two to the power of zero equal to binary one?

Probably a simple question and possibly not asked very well. What I want to know is.. In binary, a decimal value of 1 is also 1. It can be expressed as $x = 1 \times 2^0$ Question: Why is two to ...
16
votes
4answers
3k views

Is every positive nonprime number at equal distance between two prime numbers?

For example $8$ is in the middle of the interval between $5$ and $11$, $9$ is at equal distance between $7$ and $11$; $10$ between $7$ and $13$.
4
votes
7answers
651 views

What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?

The title pretty much says it all. Of course, one answer (IMO unsatisfactory) to such questions goes something like "a definition is a definition, period." In my experience, mathematical definitions ...
8
votes
6answers
1k views

Why do we call primes, and not the number one, *the atoms of numbers*?

The fundamental theorem of arithmetic asserts that we can produce every composite number from a unique set of prime multiplicands, so long as none of those primes equals one. Consequently, some ...
4
votes
4answers
7k views

What is an Integral Domain?

Okay, so almost 3 months into my abstract algebra, we just started rings. I have a few questions. A "trivial ring" is a ring with only one element. So $R={0}$ is a trivial ring. Understandable. ...

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