keiths implodes from his stupidity
-
Too funny. Now keiths has a hissy fit and sez:
Could you please prove that F(n)=2n+10 works. Sure it works to prove that you are a moron, but that is about it.
The point is that only the 2n matters- nothing else is required. Tacking on any even number on the end of the equation does nothing, ie it accomplishes the same thing that 2n accomplishes.
And these assholes accuse me of not understanding basic math...
Not to give up, keiths spews more TARD:
LoL! It maps a one-to-one correspondence. Also once in a set everything is converted to e1, e2, e3, e4,... so you don't even need a mapping function.
and:
You use the most simple equation required. Duh. Again your ignorance of math and science is not a refutation of my posts.
Too funny. Now keiths has a hissy fit and sez:
Let’s use your brilliant discovery to compare the cardinality of two sets A and B where A = {…,-3,-2,-1,0,1,2,3,…} and B = {…,-6,-4,-2,0,2,4,6,…}.
Let’s find a mapping function that gives us a bijection (a one-to-one correspondence).
F(n) = 2n works, so according to Joe Math, set A is twice as big as set B. Great! What was that twit Cantor thinking?
But wait a minute… F(n) = 2n + 10 also works. So according to Joe Math, set A has twice the cardinality of set B plus 10.
Could you please prove that F(n)=2n+10 works. Sure it works to prove that you are a moron, but that is about it.
The point is that only the 2n matters- nothing else is required. Tacking on any even number on the end of the equation does nothing, ie it accomplishes the same thing that 2n accomplishes.
And these assholes accuse me of not understanding basic math...
Not to give up, keiths spews more TARD:
No, Joe, it doesn’t accomplish the same thing. When you change the mapping function from F(n) = 2n to F(n) = 2n + 10, every single element of the first set now maps to a different element of the second set.
LoL! It maps a one-to-one correspondence. Also once in a set everything is converted to e1, e2, e3, e4,... so you don't even need a mapping function.
and:
In that case, F(n) = 2n + 0 accomplishes the same thing as F(n) = 2n + 10 which accomplishes the same thing as F(n) = 2n – 666,666 . If they all accomplish the same thing, then any one of them can be used to establish the relative cardinality of the two sets. Yet you say that only F(n) = 2n + 0 is permissible. On what basis?
You use the most simple equation required. Duh. Again your ignorance of math and science is not a refutation of my posts.
posted by Joe G @ 2:45 PM
67 Comments:
At 3:00 AM,
Unknown said…
Well, I think there is an important point.
If A = {1, 2, 3, 4 . . . . }, C = {2, 4, 6, 8 . . . . }, D = {11, 12, 12, 14 . . . }
Then you've clearly said that the cardinality of C is one half that of A . . . but still infinite. And I'm guessing you'd say the cardinality of D is 10 less than the cardinality of A but still infinite.
Which is why I want to know if you think there is a smallest infinite number? Can you just keep dividing or subtracting from the cardinality of A and keep getting infinite answers?
At 9:31 AM,
Joe G said…
Still having trouble staying on topic, I see.
And if you think there is an important point then make it.
At 1:38 PM,
Unknown said…
"Still having trouble staying on topic, I see."
Well, I thought you'd be generous when discussing such matters. Just for the intellectual fun.
"And if you think there is an important point then make it."
If your method is superior then it should be able to deal with all the situations the previous model/method dealt with and then some.
AND in the history of science and mathematics those whose have differing views know they have to argue vigorously to overthrow the established paradigm.
You are very confident in your approach to the arithmetic of infinities. I would think you would be glad to defend it, to address any and all questions about it's approach.
So . . . is there a smallest infinity?
The point being that saying yes or no has implications which need to be explored. To see if your system handles certain situations. Is your method a better fit than the accepted one. You see that surely.
At 2:14 PM,
Joe G said…
Jerad,
Cantor spent almost his entire life to this and came up with a lame "solution".
I have spent but a few hours and have demonstrated how his methodology is totally lacking in continuity. If you are going to treat sets of numbers as arbitrary objects, fine. Just don't say it's mathematics.
Take the numbers out of the brackets and it is obvious that the non-negative integers outnumber the non-negative even integers 2 to 1- FOREVER. The even integers will never catch up to the number of integers even if we go to infinity.
Infinity is not a singularity.
At 2:16 PM,
Joe G said…
And Cantor was a Creationist. Do you accept what he says about that?
At 4:18 PM,
Unknown said…
"Cantor spent almost his entire life to this and came up with a lame "solution"."
Which was then debatd and argued about by mathematicians for a long time. And was eventually accepted after it's efficacy was proven.
"I have spent but a few hours and have demonstrated how his methodology is totally lacking in continuity. If you are going to treat sets of numbers as arbitrary objects, fine. Just don't say it's mathematics."
Ah, but you haven't answered some questions which are fair and which you should be able to answer.
A new and better idea should be able to compete and explain more than the one it supposes to supplant.
"Take the numbers out of the brackets and it is obvious that the non-negative integers outnumber the non-negative even integers 2 to 1- FOREVER. The even integers will never catch up to the number of integers even if we go to infinity."
No, it is not obvious. In a basic way, the set of even integers matches up with the integers. Infinity is different from finite numbers/measures. That's the point. It takes a different kind of thinking.
"Infinity is not a singularity."
Whatever that means.
"And Cantor was a Creationist. Do you accept what he says about that?"
Anyone's ideas need to be examined and tested. And Cantor's ideas of mathematics passed the test. I do not give anyone a pass on anything.
At 4:27 PM,
Joe G said…
LoL! How is it NOT obvious? what happens beyond the LKN that might allow the even integers to catch up to the integers?
In no way, except apparently set theory, do the even integers line up with the integers.
Ah, but you haven't answered some questions which are fair and which you should be able to answer.
Ahh but YOU refuse to stay on-topic and discuss the issue at hand.
And AGAIN, give me the rest of my life, and if I consider your questions important, I will answer them.
However you don't even seem to be able to stay on-topic so I don't know wha good I will do to go any further.
At 5:16 PM,
Unknown said…
"LoL! How is it NOT obvious? what happens beyond the LKN that might allow the even integers to catch up to the integers?"
That there are just as many even integers as there are integers.
"In no way, except apparently set theory, do the even integers line up with the integers."
Good thing Set Theory is so accepted then.
"And AGAIN, give me the rest of my life, and if I consider your questions important, I will answer them."
Fine with me. As long as you don't mind falling further and further behind.
At 6:00 PM,
Joe G said…
That there are just as many even integers as there are integers.
That's impossible unless something magical happens with infinity.
Good thing Set Theory is so accepted then.
Well this part, the part about infinite sets, doesn't appear to be of any use.
As long as you don't mind falling further and further behind.
Behind what? Nothing has happened in over 100 years...
At 6:17 PM,
Joe G said…
"Take the numbers out of the brackets and it is obvious that the non-negative integers outnumber the non-negative even integers 2 to 1- FOREVER. The even integers will never catch up to the number of integers even if we go to infinity."
No, it is not obvious.
It is obvious to anyone who knows anything about numbers and math.
In a basic way, the set of even integers matches up with the integers.
FUCK YOU AND SETS. This is NOT about sets you fucking cowardly imp.
As I said you are either too syupid, too dishonest or too much of a coward to actually stay the course.
Infinity is different from finite numbers/measures.
See, you do believe infinity is magical.
That's the point. It takes a different kind of thinking.
More like a lack of thinking.
At 8:08 PM,
socle said…
Hey Joe,
What do you think of keiths' sticky-note example? It seems to me if you focus on the underlying objects in the set, it's clear those sets are the same size.
That is tied to the issue that cardinality aleph null happens when the members of a countable set can be put in one to one correspondence with the set as a whole, e.g. the evens with the natural numbers.
At 8:25 PM,
Joe G said…
Hey socle,
I haven't seen it. Can keiths put an infinite amount of numbers on a sticky note?
Is it a yellow post-it or some knock-off brand?
And yes, if the numbers don't mean anything once they are inside of {}, then Cantor is right. However that would mean that we ain't talking about math, just some arbitrary depiction of abstract groups.
Take the numbers out of the brackets and it is obvious that the non-negative integers outnumber the non-negative even integers 2 to 1- FOREVER. The even integers will never catch up to the number of integers even if we go to infinity.
Tell keiths to put that on a sticky note and staple it to his forehead.
At 8:47 PM,
socle said…
And yes, if the numbers don't mean anything once they are inside of {}, then Cantor is right.
I think I see what you are saying. It is critical that we view the sets simply as collections of elements, and not get distracted by the particular properties of those elements.
At 8:51 PM,
Joe G said…
Then we really shouldn't call it math.
And that was my point about the roller coaster hypothesis-> {e,e,e,e,...}
And if that is true then why even bother putting anything but e's in sets?
At 8:55 PM,
Joe G said…
So it's the {}, and not infinity, that is the great magical equalizer.
And that means we ain't putting integers into a set. Just a specified set of e's.
At 9:07 PM,
Joe G said…
And to top it all off, Linne was well before Cantor, so he definitely didn't use nor need cantor's set theory in order to formulate his nested hierarchy system.
At 9:31 PM,
socle said…
Then we really shouldn't call it math.
And that was my point about the roller coaster hypothesis-> {e,e,e,e,...}
And if that is true then why even bother putting anything but e's in sets?
Well, I suppose for many purposes, you actually can assume that any particular set is {e1, e2, e3, ..., en} or {e1, e2, e3, ...}, provided it is finite or countable. You would want to make all the elements different, so you could use subscripts. That's a good thing, because whatever you can prove about such a set would then apply to any other set of the same form, and you don't have to reinvent the wheel every time you work with sets whose elements are of some other type.
At 9:58 PM,
Joe G said…
Well, since the "e" is the same, we can just call each element by their numeric representation. Therefor 1,2,3,4,... on the number line remains {1,2,3,4,...} in set form. The trick is when you want to put something else in {}. 0,1,2,3,... becomes {1,2,3,4,...}. 2,4,6,8,... becomes {1,2,3,4,...}. 1,3,7,11,13,... becomes {1,2,3,4,...}
and if we want the set to be finite we just stick a number after the ...
But that format becomes an issue when we deal with sets that go to infinity to the left and right of 1. Would you use {...e1,e2,e3,...}?
And what the fuck is negative infinity? Left infinity- going to infinity, exit stage left.
At 10:07 PM,
Joe G said…
And that would mean that there isn't any such set as {0,1,2,3,...}, nor {2,4,6,8,...}- only {e1,e2,e3,e4,...} or {1,2,3,4,...} for simplicity.
No set of prime numbers, just {1,2,3,4,...}
And to say that you are comparing a set of all positive integers to a set of all positive prime numbers, would be a lie. You are comparing {e1,e2,e3,e4,...} to {e1,e2,e3,e4,...}
Now if someone would have asked me that to begin with- if {e1,e2,e3,e4,...} has the same cardinality as {e1,e2,e3,e4,...}, then I would have said yes and that would have been the end of it.
At 10:50 PM,
socle said…
Well, since the "e" is the same, we can just call each element by their numeric representation. Therefor 1,2,3,4,... on the number line remains {1,2,3,4,...} in set form. The trick is when you want to put something else in {}. 0,1,2,3,... becomes {1,2,3,4,...}. 2,4,6,8,... becomes {1,2,3,4,...}. 1,3,7,11,13,... becomes {1,2,3,4,...}
That does work for some purposes. Just to clarify, {1, 2, 3, ...} and {0, 1, 2, ...} are not equal, meaning they don't have exactly the same elements, but they do share certain properties. For example, their power sets do have the same size.
and if we want the set to be finite we just stick a number after the ...
But that format becomes an issue when we deal with sets that go to infinity to the left and right of 1. Would you use {...e1,e2,e3,...}?
Yes, that's the standard notation.
And what the fuck is negative infinity? Left infinity- going to infinity, exit stage left.
Yes, negative infinity is kind of a strange concept. IMHO, both infinity and negative infinity are most useful when used as a kind of shorthand. You could say that the sequence -1, -2, -3, ... "goes to negative infinity", meaning that if go out far enough, eventually all the remaining numbers in that list will be less than any previously specified negative number. It's actually probably less exotic than it sounds.
At 11:10 PM,
socle said…
And that would mean that there isn't any such set as {0,1,2,3,...}, nor {2,4,6,8,...}- only {e1,e2,e3,e4,...} or {1,2,3,4,...} for simplicity.
No set of prime numbers, just {1,2,3,4,...}
And to say that you are comparing a set of all positive integers to a set of all positive prime numbers, would be a lie. You are comparing {e1,e2,e3,e4,...} to {e1,e2,e3,e4,...}
As I just mentioned in my previous post, the set {1, 2, 3, ...} would not be equal to the set of primes, since they do not have the same elements, but they still share properties. Just like two different car models will be different at some level, but they probably both have 4 wheels, a transmission, etc.
There is a joke about mathematicians not being able to distinguish between a coffee cup and a donut. Obviously they are very different, but if you make a clay model of a coffee cup, you see that it can be deformed into a donut shape without tearing or forming any extra holes in it. You can also go in the reverse direction.
On the other hand, you can't form a solid ball of clay into a donut shape without punching a hole in it, so it would seem that donuts and coffee cups actually do share some properties that a solid ball does not have.
It's really the same with sets. They can be distinct, yet still have things in common.
At 11:58 PM,
Unknown said…
" 'That there are just as many even integers as there are integers.'
That's impossible unless something magical happens with infinity."
Nothing magical. Just something different than with finite sets.
" 'Good thing Set Theory is so accepted then.'
Well this part, the part about infinite sets, doesn't appear to be of any use."
Doesn't matter to me if you've not kept up with modern mathematics.
" 'As long as you don't mind falling further and further behind.'
Behind what? Nothing has happened in over 100 years…`'
Doesn't matter to me if you've not kept up with modern mathematics. Like Chaos Theory. Like Information Theory. Like Topology. Like non-Euclidean Geometries. Like hyper-real and surreal numbers.
"FUCK YOU AND SETS. This is NOT about sets you fucking cowardly imp."
Whatever. You're the one that started several threads about it.
" 'Infinity is different from finite numbers/measures.'
See, you do believe infinity is magical."
I don't think different means magical. Cantor showed there was logic and coherence. Not magical at all. But different.
" 'That's the point. It takes a different kind of thinking.'
More like a lack of thinking. "
If you can't take the heat stay out of the kitchen.
"And to say that you are comparing a set of all positive integers to a set of all positive prime numbers, would be a lie. You are comparing {e1,e2,e3,e4,...} to {e1,e2,e3,e4,...}
Now if someone would have asked me that to begin with- if {e1,e2,e3,e4,...} has the same cardinality as {e1,e2,e3,e4,...}, then I would have said yes and that would have been the end of it."
That was the point. We were just comparing sets. One of the sets had
e1 =1, e2 = 2, e3 = 3 . .. . .
The other set could be
e1 = 2, e2 = 4, e3 = 6 . . .. .
Or:
e1 = 2, e2 = 3, e3 = 5 . . . . (the primes)
Or:
e1 = 17, e2 = 34, e3 = 51 . . . .
All those sets are the same size. They are all countably infinite.
At 7:18 AM,
Joe G said…
It's all moot guys. Nested hierarchies do not rely on Cantor's set theory.
AND nested hierarchies care what is in its sets.
And sets that go to infinity may be the same size but take it out of the set and the numbers accumulated are not the same.
As I said the non-negative intefers outnumber the positive even integers 2 to 1- yes even out in infinity.
At 7:24 AM,
Unknown said…
"And sets that go to infinity may be the same size but take it out of the set and the numbers accumulated are not the same."
True. Cardinality has to do with the size of the set.
"As I said the non-negative intefers outnumber the positive even integers 2 to 1- yes even out in infinity."
Nope. The set of all positive integers is the same size as the set of even integers.
At 7:29 AM,
Joe G said…
LoL! The numbers are out of the sets.
As I said obvioulsy you have issues that make yoiu incapable of following along.
At 7:29 AM,
Joe G said…
It's all moot guys. Nested hierarchies do not rely on Cantor's set theory.
AND nested hierarchies care what is in its sets.
At 9:46 AM,
Unknown said…
"LoL! The numbers are out of the sets.
As I said obvioulsy you have issues that make yoiu incapable of following along."
Whatever makes you feel better. It doesn't change the fact that the set of all integers is the same size as the set of all even integers.
At 11:18 AM,
Joe G said…
It doesn't change the fact that the set of all integers is the same size as the set of all even integers.
And taht doesn't change the fact that outside of sets the non-negative integers outnumber the positive even integers 2-to-1.
At 11:27 AM,
Unknown said…
"And taht doesn't change the fact that outside of sets the non-negative integers outnumber the positive even integers 2-to-1."
Nope, there are the same number of integers as there are even integers.
Sets are just collections of objects. The { } notation is just convention.
At 11:29 AM,
Joe G said…
Nope, there are the same number of integers as there are even integers.
That's impossible.
At 11:48 AM,
Unknown said…
" 'Nope, there are the same number of integers as there are even integers.'
That's impossible."
Welcome to real Set Theory.
At 11:54 AM,
Joe G said…
Helloooooo! I'm not talking about Set Theory.
At 4:35 PM,
Unknown said…
"Helloooooo! I'm not talking about Set Theory."
You are when you are comparing the number of integers and the number of even integers.
Set Theory doesn't mean you have to use the { }s. It just means you're talking about collections of things.
At 5:03 PM,
Joe G said…
It's not a collection.
At 5:26 PM,
Unknown said…
"It's not a collection."
What's not a collection? The positive integers? Of course that's a collection. The positive even integers? Of course it is. Throw a dice and infinte number of times and write down the results. Is that a set/collection. You bet. How about the Real Numbers? Definitely a set/collection. I can tell what is in that set and what is not. Is it infinite? Well duh!!
At 8:56 PM,
Joe G said…
Yes, you can make the integers a set, but that takes away all of their meaning/ properties.
So I prefer to view them out of a set and part of the number line.
At 1:52 AM,
Unknown said…
"Yes, you can make the integers a set, but that takes away all of their meaning/ properties.
So I prefer to view them out of a set and part of the number line."
Far from it really. Just because you defined your set as the set of all positive integers doesn't mean you can't ask other questions about them.
For example: what is the third perfect number? What are the amicable numbers? What is the denisty of the prime numbers? What is the first number whose 'name' when written in modern English has an 'a' in it? Which numbers, in their modern representation, are palindromes? Is it true that every number greater than 4 can be expressed as the sum of two prime numbers? Are their an infinite number of prime pairs?
You know, do mathematics.
At 7:19 AM,
Joe G said…
I am not defining a set. I am no longer talking about set theory.
At 8:12 AM,
Unknown said…
"I am not defining a set. I am no longer talking about set theory."
You're talking about the positive integers. The collection of all the positive integers. That's a set.
Doesn't mean they lose any of their properties just 'cause they're in the set. The set is just the collection of things you're talking about.
I thought you took a course in this stuff?
At 8:30 AM,
Joe G said…
No, they lose their properties- that is according to you, socle and everyone else arguing against me.
And I haven't taken anything wrt set theory for over 30 years. It wasn't useful then and I didn't find any use for it throughout my life.
At 9:03 AM,
Unknown said…
"No, they lose their properties- that is according to you, socle and everyone else arguing against me."
Whatever makes you happy.
"And I haven't taken anything wrt set theory for over 30 years. It wasn't useful then and I didn't find any use for it throughout my life."
It's a very foundational and active branch of mathematics! You're not a mathematician. So I'm not surprised you don't know about the ongoing research and uses within the field.
But that doesn't make it useless.
At 9:22 AM,
socle said…
No, they lose their properties- that is according to you, socle and everyone else arguing against me.
They don't lose any of their properties, Joe. The sets {1, 2, 3, ...}, {2, 4, 6, ...}, and {e1, e2, e3, ...} are not equal.
What I said was that {1, 2, 3, ...}, {2, 4, 6, ...}, {e1, e2, e3, ...}, {x1, x2, x3, ...} and so on all have some properties in common, such as cardinality.
At 9:48 AM,
Joe G said…
The sets {1, 2, 3, ...}, {2, 4, 6, ...}, and {e1, e2, e3, ...} are not equal.
What's the difference?
At 9:48 AM,
Joe G said…
Geez Jerad, strange that you cannot tell me about any uses- especially the part of infinite countable sets having the same cardinality...
At 9:55 AM,
Joe G said…
You're not a mathematician.
Perhaps not. However I deal with reality and useful things.
At 10:09 AM,
socle said…
What's the difference?
Sets A and B are equal if and only if A is a subset of B and B is a subset of A.
{1, 2, 3, ...} is not a subset of {2, 4, 6, ...} because 1 is an element of the first set but not of the second, therefore {1, 2, 3, ...} is not equal to {2, 4, 6, ...}.
IIRC, at the beginning of the discussion, everyone agreed that {2, 4, 6, ...} is a proper subset of {1, 2, 3, ...}, which means {2, 4, 6, ...} is not equal to {1, 2, 3, ...} by definition.
The third set is disjoint from the other two, so it cannot be equal to either.
At 10:14 AM,
Joe G said…
OK so when it suits people there is a difference, otherwise it is all {e1,e2,e3,e4,...}
Is that about right?
At 10:28 AM,
socle said…
OK so when it suits people there is a difference, otherwise it is all {e1,e2,e3,e4,...}
Is that about right?
Not exactly. Given two sets, they are either equal or not equal, regardless of whether it suits anyone or not.
At 10:38 AM,
Joe G said…
They can be equal in more than one way, regardless of whether or not it suits anyone.
At 11:04 AM,
socle said…
They can be equal in more than one way, regardless of whether or not it suits anyone.
I'm not clear on the meaning of this. Are you saying that two sets can simultaneously be equal and not equal?
At 11:12 AM,
Joe G said…
Two sets can be equal in size and not equal in properties- simultaneously.
At 11:14 AM,
Joe G said…
IIRC, at the beginning of the discussion, everyone agreed that {2, 4, 6, ...} is a proper subset of {1, 2, 3, ...}, which means {2, 4, 6, ...} is not equal to {1, 2, 3, ...} by definition.
And also by definition a proper subset has fewer elements than its proper superset. And yet...
At 12:03 PM,
Unknown said…
"Two sets can be equal in size and not equal in properties- simultaneously."
Correct!
"And also by definition a proper subset has fewer elements than its proper superset. And yet…"
Incorrect! NOT part of the definition of proper subset.
At 12:41 PM,
socle said…
Well, I'm relieved to see that you are not saying that two sets can simultaneously be equal and not equal. That shouldn't happen in ZFC.
At 7:26 AM,
Joe G said…
Proper subset:
A proper subset of a set , denoted , is a subset that is strictly contained in and so necessarily excludes at least one member of . The empty set is therefore a proper subset of any nonempty set.
For example, consider a set . Then and are proper subsets, while and are not.
At 7:29 AM,
Joe G said…
ask Dr Math:
If every member of one set is also a member of a second set, then the first set is said to be a subset of the second set. Usually, it turns out that the first set is smaller than the second, but not always. The definition of "subset" allows the possibility that the first set is the same as (equal to) the second set. But a "proper subset" must be smaller than the second set. (bold added)
At 10:31 AM,
Unknown said…
"A proper subset of a set , denoted , is a subset that is strictly contained in and so necessarily excludes at least one member of . The empty set is therefore a proper subset of any nonempty set."
Yeah but it doesn't mean they aren't the same size if they're infinitely large!!
"If every member of one set is also a member of a second set, then the first set is said to be a subset of the second set. Usually, it turns out that the first set is smaller than the second, but not always. The definition of "subset" allows the possibility that the first set is the same as (equal to) the second set. But a "proper subset" must be smaller than the second set."
I agree if the sets are finite. Check Dr Math (???) to see if 'he' covers that case.
At 10:33 AM,
Unknown said…
Gee whiz Joe, Dr Math is so elementary!! It doesn't go vary far 'up' the mathematical ediface at all!!
But I did find this:
"There is no largest number! Why? Well, 1,000,000,000 (1 billion) can't be the largest number because 1 billion + 1 is bigger - but that is true for any number you pick. You can choose any big number and I can make a bigger one just by adding 1 to it."
At 10:34 AM,
Joe G said…
Again Jerad is caught mesmerized by infinity...
At 10:35 AM,
Joe G said…
Gee whiz Jerad, I said the LKN continues to change.
Again your inability to follow along is growing tiresome.
Be back later...
At 10:41 AM,
Unknown said…
Oh wait, there was a bit more:
"Now for the fun part! Even though infinity is not a number, it is possible for one infinite set to contain more things than another infinite set. Mathematicians divide infinite sets into two categories, countable and uncountable sets. In a countably infinite set you can 'number' the things you are counting. You can think of the set of natural numbers (numbers like 1,2,3,4,5,...) as countably infinite. The other type of infinity is uncountable, which means there are so many you can't 'number' them. An example of something that is uncountably infinite would be all the real numbers (including numbers like 2.34.. and the square root of 2, as well as all the integers and rational numbers). In fact, there are more real numbers between 0 and 1 than there are natural numbers (1,2,3,4,...) in the whole number line! See One infinity larger than another? for more information."
And so on. Sounds like Dr Math agrees with me!!
At 10:42 AM,
Unknown said…
"Gee whiz Jerad, I said the LKN continues to change."
Which is why THERE ISN'T ONE!!
"Again your inability to follow along is growing tiresome."
I'm following along just fine thanks!
"Be back later…"
No worries. Late afternoon here so will be doing other stuff soon.
At 10:49 AM,
socle said…
Joe,
What is this LKN you are referring to? Do you have a definition? I've never heard of such a thing.
At 11:06 AM,
Joe G said…
LKN= Largest Known Number
It was my impression that there was a computer keeping track of such a thing. Perhaps not.
At 2:05 AM,
Unknown said…
"LKN= Largest Known Number
It was my impression that there was a computer keeping track of such a thing. Perhaps not."
There's no point to that.
As I said there is the largest known prime number but even that changes pretty often.
At 7:07 AM,
Joe G said…
Who the fuck are you to say there is no point of keeping track of the LKN?
Obvioulsy there isn't any point of saying the cardinality of countable and infinite sets are the same...
At 10:55 AM,
Unknown said…
"Who the fuck are you to say there is no point of keeping track of the LKN?"
If you can't have a civilised conversation then I'm going to quit.
"Obvioulsy there isn't any point of saying the cardinality of countable and infinite sets are the same…"
Whatever you say Joe.
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