What is your favorite number (single digit integer*), and why?

[Kyriakos]

Well, in that case I'm going with i: the square root of minus 1.

Or I imagine I will.

II rc the square root of -1 is not having to be 'i'*, although 'i' raised to the second power equals -1

*I don't recall now if 'i' in algebra is ever there as tied to a solution, if it is not at least raised to the second power. I hate so-called 'complex' numbers, and have an aversion to 'i' too

'i' only has four values, raised to any power:

i= i
i2= -1
i3= -i
i4=1

then each power returns to the first four positions, ie i5=i1, i6=i2 etc

 

[Borachio]

Complex analysis! Gah!

I've not really studied it, tbh. But they tell me it's interesting. If a little complex.

But sure, i x i = -1 and -1 x -1 = 1.

And of course e^(i*pi) + 1 = 0. Interestingly. Thank you, Mr Euler.

 

[MilesGregarius]

The best digit is 1.

Out of 1 you can create all the other ones. 1 is #1

But one is the loneliest number.

(Although two can be as bad as one.)

 

[Perfection]

tie between 1 and 0 because they are both so extremely interesting.

 

[Kennigit]

incorrect

what is i^(1/2)

 

[nc-1701]

Yes, as in eg 3/0.

Yes? I'm not sure I follow...

Don't you need both 0 and 1 for any meaningful algebra?

More or less, 0 and 1 are the additive and multiplicative identities, which allow things like inverses to make. In general you can have a ring with no multiplicative identity, but all rings have an additive identity. You can do (somewhat) meaningful algebra in a ring, so I guess all you need is zero

1 is an important integer since it is a generator of the integers (so is -1).

incorrect

what is i^(1/2)

Well integer powers of i do form a cycle of length 4... And other powers will also form cycles...

Anyway I'll bite i^(1/2) = (sqrt2 +isqrt2)/2

 

[Borachio]

i^(1/2) = -1^(1/4)

Nope. I really don't know. What's the answer?

 

[nc-1701]

i^(1/2) = -1^(1/4)

Nope. I really don't know. What's the answer?

I posted it above... nth roots of i are easy to get using Euler's formula.

e^(i*pi/2)=i

So

e^(i*pi/2n)=i^(1/n)

 

[Kyriakos]

Yes? I'm not sure I follow...

0, as noted in the OP, is not always something defined, and thus neither is it integral at those times. Eg if you try to ask how many times does 0 fit in 3 (3/0), the answer is not currently meaningful cause zero is seen as zero regardless of it being a void or a quantity which happens to be axiomatically not part of that set. For example you could liken 3/0 to asking how many times a line fits inside a plane. The answer is not definable, for by axioms the line gets seen as lost in the continuum of the plane.

(likewise for a singular point in relation to a line, or a plane in relation to a volume, etc).

So, as noted, zero is not an integer, but a sort of not-fixed-at-all-times notion.

 

[nc-1701]

Zero is what we call the additive identity in a ring or field, in this sense it always exists and absolutley is an integer (since the integers are a ring), what is special about zero is that it does not have a multiplicative inverse. This is where you are getting confused by 3/0... Division is not an algebraically defined operation, it is a shorthand for multiplication by the inverse. Zero is the only real (or even complex) number without an inverse, therefore we can't multiply by it's inverse, hence we can't divide by zero.
It's worth noting that most integers do not have multiplicative inverses without extending the field to the rational numbers, hence integers being a ring and not a field. In the algebraic notion of numbers, zero is always very clearly defined. In a non algebraic notion of numbers the concept of integer isn't really meaningful outside of counting, where again 0 is clearly defined.

 

[Kyriakos]

Zero is what we call the additive identity in a ring or field, in this sense it always exists and absolutley is an integer (since the integers are a ring), what is special about zero is that it does not have a multiplicative inverse. This is where you are getting confused by 3/0... Division is not an algebraically defined operation, it is a shorthand for multiplication by the inverse. Zero is the only real (or even complex) number without an inverse, therefore we can't multiply by it's inverse, hence we can't divide by zero.
It's worth noting that most integers do not have multiplicative inverses without extending the field to the rational numbers, hence integers being a ring and not a field. In the algebraic notion of numbers, zero is always very clearly defined. In a non algebraic notion of numbers the concept of integer isn't really meaningful outside of counting, where again 0 is clearly defined.

Any source for this matter-of-fact info you posted? I mean Cantor is cancelled for good now, and you did not even have to allude to more stuff than division in arithmetic.

(pls offer a source of note presenting the definition you just posted, or one close enough to it).

 

[Steph]

8, because if you look at it sideways it's the symbol of infinity.

 

[classical_hero]

tie between 1 and 0 because they are both so extremely interesting.

It's only a binary choice.

Mine is 56ish.

 

[Tahuti]

Call me an idiot, but I always had a liking for 2. Probably for being the only even prime number.

 

[warpus]

Kyriakos, an integer is just a number that can be written without a fractional component.

0 is an integer, I'm not sure what mathematician would disagree with that.

 

[dgfred]

8, because if you look at it sideways it's the symbol of infinity.

Or eyeballs .

 

[nc-1701]

Any source for this matter-of-fact info you posted? I mean Cantor is cancelled for good now, and you did not even have to allude to more stuff than division in arithmetic.

(pls offer a source of note presenting the definition you just posted, or one close enough to it).

That's the just some very basic Abstract Algebra groundwork, I'll PM you with some more information so as to not derail your thread with it.

 

[Lohrenswald]

My favorite single digit whole number is 6.
Firstly because hexagons are da graetest polygon.
Secondly, 6 is one of the most important numbers in the whole sumerian system. 3 and 4 may arguably be more important, but I don't care that much for 3, and 4 doesn't quite cut it.

Related: I don't see how people are so fascinated by prime numbers. You can't divide them into whole numbers - they have no structure, and that makes them boring (unlike say 12, which is great)

 

[Lights]

I like 4's shape. It isn't curved and it isn't dull as 1 or 7

 

[nc-1701]

Related: I don't see how people are so fascinated by prime numbers. You can't divide them into whole numbers - they have no structure, and that makes them boring (unlike say 12, which is great)

Prime numbers are the structure