keiths, so stupid it hurts
-
keiths sez:
All of the odds numbers were elements of the first set. They have been removed from the first set in order to form the second set.
Where did all of the odd numbers go if you didn't remove them? Or are you really that fucking stupid?
But anyway-
That fact is because the first set's cardinality is 2x that of the second set. Again my methodology works.
Then he sez:
No, you stupid fuck. All you are doing by using F(n)=2n is converting the first set into the second and then saying they are now equal. The reason that F(n)=2n works is because teh first set's cardinality is 2x that of the second set.
You people are so fucking stupid it hurts.
keiths the piece of sjit TARD responds:
No, keiths, the odd numbers are NOT there. They have been removed by your math, dumbass.
All of the odd numbers are gone, dumbass.
I said
No, you stupid fuck. All you are doing by using F(n)=2n is converting the first set into the second and then saying they are now equal.
Not another TARDgasm- AGAIN equal wrt to CONTEXT means the same cardinality. And BTW, converting one set into the other means they are equal, in size AND they also have the exact same members. As I said, you are obvioulsy an imbecile.
And if you convert the first set into the second then you have changed everything. You are no longer trying to compare two different sets. You are now comparing one set against itself.
keiths sez:
The fact is that {1,2,3,…} can be converted into {2,4,6,…} without adding or removing any elements. You simply multiply each element by 2.
All of the odds numbers were elements of the first set. They have been removed from the first set in order to form the second set.
Where did all of the odd numbers go if you didn't remove them? Or are you really that fucking stupid?
But anyway-
The fact is that {1,2,3,…} can be converted into {2,4,6,…} without adding or removing any elements. You simply multiply each element by 2.
That fact is because the first set's cardinality is 2x that of the second set. Again my methodology works.
Then he sez:
You claim that {1,2,3,…} is twice as big as {2,4,6,…}. If that were true, then it would be impossible to map {1,2,3,…} to {2,4,6,…} using F(n) = 2n, because we would exhaust the elements of {2,4,6,…} before all of the elements in {1,2,3,…} had been mapped.
No, you stupid fuck. All you are doing by using F(n)=2n is converting the first set into the second and then saying they are now equal. The reason that F(n)=2n works is because teh first set's cardinality is 2x that of the second set.
You people are so fucking stupid it hurts.
keiths the piece of sjit TARD responds:
The odd numbers are still there, Joe. It’s just that they’ve been doubled. The original set was {1,2,3,4,5,…} and the new set is {1+1, 2+2, 3+3,4+4,5+5,…}, which of course is the same as {2,4,6,8,10,…}. I didn’t remove any elements; I doubled each existing element and left it in place.
No, keiths, the odd numbers are NOT there. They have been removed by your math, dumbass.
Which elements magically disappeared, Joe?
All of the odd numbers are gone, dumbass.
I said
No, you stupid fuck. All you are doing by using F(n)=2n is converting the first set into the second and then saying they are now equal.
No, I’m converting the first set into the second and saying that they have the same cardinality.
Not another TARDgasm- AGAIN equal wrt to CONTEXT means the same cardinality. And BTW, converting one set into the other means they are equal, in size AND they also have the exact same members. As I said, you are obvioulsy an imbecile.
And if you convert the first set into the second then you have changed everything. You are no longer trying to compare two different sets. You are now comparing one set against itself.
posted by Joe G @ 10:37 PM
15 Comments:
At 2:26 AM,
Unknown said…
Let's say you have all the elements of {1, 2, 3, 4, . . . } lined up in front of you. You pick them up, one at a time and convert them to twice their original amount and put them back in the same place. The line of elements never gets any bigger or smaller. It stays the same size.
The two sets are the same size.
Based on your method I assume you would say the cardinality of {1, 2, 3, . . . } + cardinality of {2, 4, 6, . . . } would be 1.5 X cardinallity of the first set.
Is there a smallest infinite number?
At 9:50 AM,
Joe G said…
And again Jerad the coward cannot stay on-topic.
What the fuck is wrong with you Jerad?
What happened to all of the odd numbers Jerad?
At 2:10 PM,
Unknown said…
I'm just saying . . . if you have an infinitly long line of balls numbered 1, 2, 3 . . . and you pick each one up, one at a time, and change the number to its double and put it back the line of balls stays the same length. You don't have to shift any balls left or right.
Is there a smallest infinity?
At 2:15 PM,
Joe G said…
What happened to all of the odd numbers, Jerad?
At 3:29 PM,
Unknown said…
"What happened to all of the odd numbers, Jerad?"
They got mapped to 2 times their value.
But I didn't have to collapse or expand my line of numbers. I just changed their labels.
Is there a smallest infinity?
At 7:19 PM,
Joe G said…
They got mapped to 2 times their value.
No, they were removed. 2 times their value was already in the set.
Is there a smallest infinity?
If it's possible. But what does that have to do with anything we are discussing?
At 2:38 AM,
Unknown said…
The values were removed but the line of numbers stays the same size.
The existence of a smallest infinity is crucial.
If you say the set A = {1, 2, 3, 4 . . . . } has (an unspecified) infinite cardinality and C = {2, 4, 6, 8 . . . } has an infinite cardinality that is one half of A's. And the cardinality of X = {x, 2x, 3x . . . } would have cardinality 1/x times A's.
What if x is what you call the largest known number? Or 1/LKN?
Also, how do you handle infinite sets that are not easily innumerated as multiples of A? Like the set of all prime numbers? Or the set of the digits of Pi? What are their cardinalities?
At 9:44 AM,
Joe G said…
The values were removed but the line of numbers stays the same size.
Yes, the LINE stays the same size but the the amount of numbers on that line.
The existence of a smallest infinity is crucial.
Show me where Cantor said that. All he has is small infinity (countable) and large infinity (uncountable).
If you say the set A = {1, 2, 3, 4 . . . . } has (an unspecified) infinite cardinality and C = {2, 4, 6, 8 . . . } has an infinite cardinality that is one half of A's. And the cardinality of X = {x, 2x, 3x . . . } would have cardinality 1/x times A's.
Yup.
What if x is what you call the largest known number? Or 1/LKN?
What if?
Also, how do you handle infinite sets that are not easily innumerated as multiples of A? Like the set of all prime numbers?
Then you would have to do some figuring OR just say that one is greater than/ leas than/ equal to the other.
Or the set of the digits of Pi? What are their cardinalities?
Infinite.
At 1:48 PM,
Unknown said…
"Yes, the LINE stays the same size but the the amount of numbers on that line."
I'll not call you on that typo. But the point is: how can you say the amount of numbers on one line is bigger than the amount of numbers on another line IF the length of the lines are the same?
"Show me where Cantor said that. All he has is small infinity (countable) and large infinity (uncountable)."
And more actually. Look up Cantor's Continuum Hypothesis.
" 'Or the set of the digits of Pi? What are their cardinalities?'
Infinite."
Yes but of what size?
For example, the Cantor model says the cardinality of the primes is the same as the cardinality of the positive integers. What do you say?
You've got to do better than Cantor if you want to have a better theory.
At 2:05 PM,
Joe G said…
Typos are all you can call me on. LoL!
But the point is: how can you say the amount of numbers on one line is bigger than the amount of numbers on another line IF the length of the lines are the same?
I told you how already.
For example, the Cantor model says the cardinality of the primes is the same as the cardinality of the positive integers. What do you say?
I say Cantor is wrong and provided the reasonoing, which you seem to be ignoring as if your willful ignorance is some sort of refutation.
BTW Cantor's continuum hypothesis is the subject of much debate.
At 4:29 PM,
Unknown said…
"I say Cantor is wrong and provided the reasonoing, which you seem to be ignoring as if your willful ignorance is some sort of refutation."
Show me, by answering questions about the cardinality of the primes and the digits of Pi and so forth that Cantor is wrong. Show me your system is rigorous and coherent and explains things.
Don't run away and get belligerent. Stay and fight your corner. That's the way science and mathematics works. If you've got the goods then you fight to the death.
"BTW Cantor's continuum hypothesis is the subject of much debate."
Glad to see you're trying to catch up!
And what do you say? Is the cardinality of the real numbers greater than the cardinality of the integers? And why do you think so.
At 6:13 PM,
Joe G said…
Umm I don't have to answer any questions. My reasoning stands as it is.
And I am fighting. All you do is ignore what I post. You don't seem to undersatnd that we have to resolve what is in front of us FIRST, bbefore moving on.
Is the cardinality of the real numbers greater than the cardinality of the integers? And why do you think so.
Yes it is and I have explained why.
I have explained why the non-negative integers is greater than the positive even integers. You choked on that, too.
At 12:04 AM,
Unknown said…
"Umm I don't have to answer any questions. My reasoning stands as it is."
No, you don't. Unless you want to show people that it works.
"And I am fighting. All you do is ignore what I post. You don't seem to undersatnd that we have to resolve what is in front of us FIRST, bbefore moving on."
I thought we were talking about the cardinality of sets.
" 'Is the cardinality of the real numbers greater than the cardinality of the integers? And why do you think so.'
Yes it is and I have explained why."
Did you? The REAL numbers. The ones that are the rational numbers and stuff like root 2 and Pi and e that are not rational numbers.
"I have explained why the non-negative integers is greater than the positive even integers. You choked on that, too."
Not according to just about everyone else on the planet whose studied mathematics.
At 7:27 AM,
Joe G said…
I have explained why the non-negative integers is greater than the positive even integers. You choked on that, too.
Not according to just about everyone else on the planet whose studied mathematics.
Really? So they think that something magical happens out in infinity to allow the even numbers to catch up?
There isn't any one-to-one correspondence once the numbers atre out of the {} and on the number line.
And it is all moot anyway as nested hierarchies don't care about Cantor.
At 9:50 AM,
Unknown said…
"Really? So they think that something magical happens out in infinity to allow the even numbers to catch up?"
Nope. That's not the point. The point is that the set of integers is the same size (has the same number of elements) as the set of even integers.
"There isn't any one-to-one correspondence once the numbers atre out of the {} and on the number line."
I've got two infinite sets and a one-to-one mapping between them so they are the same size.
"And it is all moot anyway as nested hierarchies don't care about Cantor."
Does that mean you're giving up on your method of infinities?
Post a Comment
<< Home