02 Sep 2015, 11:00 am
slave wrote:
Rudin wrote:
slave wrote:
naturalplastic wrote:
What's the difference between a "transcendental number", and an "irrational" number?
also think 'ratio' when you think of irrational numbers as oppose to irrational as defined as being unreasonable
an irrational number is any real number than cannot be expressed as a RATIO of integers
hope that adds to Rudin's good explanation
Slave, I need to ask you something.
Do you think my signature is too long and making threads longer? Should I shorten it?
Sry, Rudin, I just read this right now.
I would have suggested removing the double spacing to attenuate it a little, but it wasn't bothering me.
Mine is longer than most users so I can hardly criticize anyone else.
I see that you have altered it, so my response is effectively moot.
Okay. I have changed it because someone told me to. I like my new one more (not better, more).
06 Sep 2015, 2:59 pm
I like putting them into a diagram, makes it easier for me to get an overview.
I'm not a 100% sure about the definitions, but is the following correct :
Real numbers
Quote:
Any numbers we can actually write ( including rounded off numbers irrational numbers )
Integer
Quote:
Any whole numbers
[ul]Natural[/ul]
Quote:
Any positive integer, including 0
Rational
Quote:
Anything that can be written as a ratio, including ratios that becomes integers like 5 / 1 = 5 or -4 / 1 = -4
Irrational numbers
Quote:
Numbers that can't be expressed as a ratios.
There are two types of irrational numbers : real algebraic and transcendental
There are two types of irrational numbers : real algebraic and transcendental
Real algebraic
Quote:
Irrational numbers that can be expressed using roots for instance square root of 2
Transcendental
Quote:
Irrational numbers that can't be expressed using roots ( so any irrational number that's not real algebraic)
Imaginary numbers
Quote:
Numbers we can't express, either exact or estimated using regular numbers. An example of this is the square root of -4.
We can't express this since the square root of 4 ( positive ) is 2 * 2. If we change the prefix we get -2 * -2 = 4. So we'd need a different kind of number so that 2i * 2i = -4
This is completely different from any real numbers, including irratioanal numbers like π which we can write as ~3.141592653....
We can't express this since the square root of 4 ( positive ) is 2 * 2. If we change the prefix we get -2 * -2 = 4. So we'd need a different kind of number so that 2i * 2i = -4
This is completely different from any real numbers, including irratioanal numbers like π which we can write as ~3.141592653....
Complex number
Quote:
Any numbers that can be expressed as x = a + bi, where a and b are real numbers. All real and imaginary numbers are complex numbers.
06 Sep 2015, 8:36 pm
morslilleole wrote:
I like putting them into a diagram, makes it easier for me to get an overview.
I'm not a 100% sure about the definitions, but is the following correct :
Real numbers
Integer
[ul]Natural[/ul]
Rational
Irrational numbers
Real algebraic
Transcendental
Imaginary numbers
Complex number
I'm not a 100% sure about the definitions, but is the following correct :
Real numbers
Quote:
Any numbers we can actually write ( including rounded off numbers irrational numbers )
Integer
Quote:
Any whole numbers
[ul]Natural[/ul]
Quote:
Any positive integer, including 0
Rational
Quote:
Anything that can be written as a ratio, including ratios that becomes integers like 5 / 1 = 5 or -4 / 1 = -4
Irrational numbers
Quote:
Numbers that can't be expressed as a ratios.
There are two types of irrational numbers : real algebraic and transcendental
There are two types of irrational numbers : real algebraic and transcendental
Real algebraic
Quote:
Irrational numbers that can be expressed using roots for instance square root of 2
Transcendental
Quote:
Irrational numbers that can't be expressed using roots ( so any irrational number that's not real algebraic)
Imaginary numbers
Quote:
Numbers we can't express, either exact or estimated using regular numbers. An example of this is the square root of -4.
We can't express this since the square root of 4 ( positive ) is 2 * 2. If we change the prefix we get -2 * -2 = 4. So we'd need a different kind of number so that 2i * 2i = -4
This is completely different from any real numbers, including irratioanal numbers like π which we can write as ~3.141592653....
We can't express this since the square root of 4 ( positive ) is 2 * 2. If we change the prefix we get -2 * -2 = 4. So we'd need a different kind of number so that 2i * 2i = -4
This is completely different from any real numbers, including irratioanal numbers like π which we can write as ~3.141592653....
Complex number
Quote:
Any numbers that can be expressed as x = a + bi, where a and b are real numbers. All real and imaginary numbers are complex numbers.
Did you make that graphic?!
if so, WELL DONE
I have seen many charts with that content but never any with such a pleasing form.
May I save it for personal use?
07 Sep 2015, 12:04 am
slave wrote:
morslilleole wrote:
...
Did you make that graphic?!
if so, WELL DONE
I have seen many charts with that content but never any with such a pleasing form.
May I save it for personal use?
Nah, I don't have the skills to make things like that. I just found it by Googling "number types venn diagram" or something like that.
07 Sep 2015, 8:29 am
That IS a good diagram.
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
07 Sep 2015, 9:14 am
naturalplastic wrote:
That IS a good diagram.
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
All imaginary and real numbers are by definition complex numbers.
A number, z, is said to be complex if z=a+bi where i is the imaginary unit and a,b are real numbers. If you set a=0 then, by definition, it's still a complex number. If you set b=0, it's still a complex number.
07 Sep 2015, 11:44 am
Rudin wrote:
naturalplastic wrote:
That IS a good diagram.
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
All imaginary and real numbers are by definition complex numbers.
A number, z, is said to be complex if z=a+bi where i is the imaginary unit and a,b are real numbers. If you set a=0 then, by definition, it's still a complex number. If you set b=0, it's still a complex number.
So the phrase "complex number" is just a synonym for "number"?
What is an example of a "simple number" (ie a number that is not complex)?
07 Sep 2015, 11:58 am
morslilleole wrote:
slave wrote:
morslilleole wrote:
...
Did you make that graphic?!
if so, WELL DONE
I have seen many charts with that content but never any with such a pleasing form.
May I save it for personal use?
Nah, I don't have the skills to make things like that. I just found it by Googling "number types venn diagram" or something like that.
Well, I'm glad you shared it anyway.
Thanks again
07 Sep 2015, 12:05 pm
naturalplastic wrote:
Rudin wrote:
naturalplastic wrote:
That IS a good diagram.
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
All imaginary and real numbers are by definition complex numbers.
A number, z, is said to be complex if z=a+bi where i is the imaginary unit and a,b are real numbers. If you set a=0 then, by definition, it's still a complex number. If you set b=0, it's still a complex number.
So the phrase "complex number" is just a synonym for "number"?
What is an example of a "simple number" (ie a number that is not complex)?
Well, yes.
Naturals⊂Integers⊂Rationals⊂Algebraic reals⊂Reals⊂Complex
Yes there are numbers that are not complicated. The set of said numbers are "larger" than the complex numbers and the complex numbers are inside of these numbers. They are called surreal and hyperreal numbers.
Here is a diagram to help you understand the surreal numbers:
Surreal numbers have a different notation {a|b}. I'll explain these later in an edit, I must go.
Last edited by Rudin on 07 Sep 2015, 12:17 pm, edited 1 time in total.
07 Sep 2015, 12:12 pm
naturalplastic wrote:
Rudin wrote:
naturalplastic wrote:
That IS a good diagram.
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
All imaginary and real numbers are by definition complex numbers.
A number, z, is said to be complex if z=a+bi where i is the imaginary unit and a,b are real numbers. If you set a=0 then, by definition, it's still a complex number. If you set b=0, it's still a complex number.
So the phrase "complex number" is just a synonym for "number"?
What is an example of a "simple number" (ie a number that is not complex)?
Definition of 'complex'
1.
a. Consisting of interconnected or interwoven parts; composite: complex equipment with multiple components.
b. Composed of two or more units: a complex carbohydrate.
So I think it's called complex because you can express it like Rudin described. I'm guessing they wanted a definition that would cover nearly all numbers.
Ironically, there are more complex numbers like quarternions. It has three different kinds ( I think ) imaginary numbers. So that i2 = j2 = k2 = ijk = −1. I want to learn more about them, but right now they're beyond my comprehension. They're also non-commutative, meaning the order in which you multiply them matters so for instance ij = k, but ji = −k.
07 Sep 2015, 2:06 pm
26 Sep 2015, 1:26 pm
26 Sep 2015, 1:49 pm
26 Sep 2015, 3:41 pm
26 Sep 2015, 10:23 pm
seaweed wrote:
http://www.visualnews.com/2013/07/09/the-art-of-pi-a-colorful-data-visualization/
Oh yeah!
I saw that one before...it is AWESOME!! !
27 Sep 2015, 9:51 am
naturalplastic wrote:
Rudin wrote:
naturalplastic wrote:
That IS a good diagram.
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
Am no mathematician, but I seriously doubt that "all real, and imaginary numbers, are complex numbers".
As I understand it:neither real numbers, nor imaginary numbers, are "complex numbers".
from looking it up on Wiki "complex numbers" seem to be the products of miscegenation between real numbers, and imaginary numbers. Hybrids that occur on the Cartesian Plain at the intersections of the points on the real, and the imaginary axis'.
Like a horse getting it on with a unicorn, and then having a part imaginary, and part real offspring (a "complex colt"?)
All imaginary and real numbers are by definition complex numbers.
A number, z, is said to be complex if z=a+bi where i is the imaginary unit and a,b are real numbers. If you set a=0 then, by definition, it's still a complex number. If you set b=0, it's still a complex number.
So the phrase "complex number" is just a synonym for "number"?
What is an example of a "simple number" (ie a number that is not complex)?
No, "complex number" is not just a synonym for number. It's the set of numbers that include the square roots of negative numbers and a bigger set than the set we call the real numbers. You're getting confused about the common language usage of the word "complex". The complex numbers have a precise mathematical definition.
