Intelligent Reasoning

Promoting, advancing and defending Intelligent Design via data, logic and Intelligent Reasoning and exposing the alleged theory of evolution as the nonsense it is. I also educate evotards about ID and the alleged theory of evolution one tard at a time and sometimes in groups

Sunday, May 26, 2013

How to Determine the Cardinality of sets that go to Infinity

-
Thanks to the volume of evoTARDgasms wrt set theory, I have been able to determine how to figure out the relative cardinality wrt two sets that go to infinity.

The cardinality is determined by the mapping function.

For example the mapping function F(n)=2n, means that one set has 2x the cardinality of the other set.

The funny part is that has been right in front of their silly faces for over 100 years and no one could spot it. They thought they were mapping a one-to-one corresponce. However that "mapping"  just means they made each set equal to the other, equal in size as well as equal in membership and the equation is the actual difference in cardinality between the two original sets.

I see that keiths can only laugh at my proposal. Small minds tend to laugh at things that are out of their depth. Thanks keiths. Everything you post proves that I am correct and you are an imbecile.

• At 2:08 PM, Unknown said…

Hmmm . . .

How about an infinite set generated by randomly selecting with replacement words from the Oxford English Dictionary?

Or the set comprising {0.1, 0.2, 0.3, . . . . 0.9, 0.10, 0.11, . . . 0.19, 0.20 . . . } Some of the elements are equivalent numerically.

Or the set comprising {3, 1, 4, 1, 5 . . . } the digits of Pi.

What are their cardinalities?

• At 2:18 PM, Joe G said…

Do the math, Mr Math MS bluffer.

Obvioulsy you are too stupid to comprehend what you read. Perhaps you can do better at math.

HINT: What are you mapping your sets to? My methodology in the OP comprises of comparing two sets that go to infinity and using the mapping to find the relative cardinality.

• At 3:27 PM, Unknown said…

I would map all three sets I innumerated to the countably infinite positive integers so they'd have the same cardinality as that set.

But there's no numerical constant generated in doing so. At least not with the first and third example.

So . . . what does your method give as an answer?

• At 6:50 PM, Rich Hughes said…

Oh Joe, your bluffing history is well documented HERE.

• At 7:15 PM, Joe G said…

And cowardly Richie chimes in with more cowardice

• At 7:17 PM, Joe G said…

I would map all three sets I innumerated to the countably infinite positive integers so they'd have the same cardinality as that set.

Show the equation(s)

• At 2:29 AM, Unknown said…

Example one:

1 <-> first word picked

2 <-> second word picked

3 <-> third word picked

(as the random selection is done with replacement words could appear on the list more than once)

Example 2:

1 <-> 0.1

2 <-> 0.2

3 <-> 0.3

etc

Example 3:

1 <-> 3

2 <-> 1

3 <-> 4

4 <-> 1

etc.

In all three cases one countably infinite set is matched one-to-one with another set. I don't know what the, say, 3567th word will be but I can get a computer to gnerate a list quickly. Clearly that mapping will change depending on the random selection. The other two are static.

What does your method say? What is the cardinality of the set of the digits of Pi? Or the digits of e? Or the digits of the square root of 2?

• At 9:46 AM, Joe G said…

In all three cases one countably infinite set is matched one-to-one with another set.

No matching. To match means the two objects on eiether end of the matching line are the same.

So no equations- I asked for equations, Mr Math.

• At 1:42 PM, Unknown said…

"No matching. To match means the two objects on eiether end of the matching line are the same."

How can you match the end of infinite sets? You can show a one-to-one correspondence between elements of one set to another. And, if you can do that, showing that noting gets letf out of either set, that the sets must be the same size.

"So no equations- I asked for equations, Mr Math."

Ummm . . . you don't need "equations" to define functions. Or mappings.

• At 2:08 PM, Joe G said…

How can you match the end of infinite sets?

There aren't any ends. However you can determine if the numbers will be the same at any point in time by looking at the finite and if tehre is a pattern, using it to extend to infinity.

Again infinity isn't magical. It is just more of the same if a pattern is found in the finite.

And your mapping is just arbitrary. And has nothing to do with math.

• At 4:24 PM, Unknown said…

"There aren't any ends. However you can determine if the numbers will be the same at any point in time by looking at the finite and if tehre is a pattern, using it to extend to infinity."

It's not a question of if the numbers are the same! It's a question of whether or not there are the same number of things!! Infinity doesn't work like the finite. That's the point!!

Why do you think Cantor's ideas were initially met with such animosity? It's becuase even mathematicians found them difficult and counterintuitive.

"Again infinity isn't magical. It is just more of the same if a pattern is found in the finite."

No, it isn't magical. But it's not the same as the finite. And the pattern in the finite, in my examples, is that there is a one-to-one correspondence between the integers and the even integers. All the way down the line.

"And your mapping is just arbitrary. And has nothing to do with math."

It has everything to do with math. Real math. Math is more than just formulas and equalities. As you should know having taken a Calculus course and a course in Set Theory.

• At 12:27 AM, Unknown said…

Who said mathematics was just about numbers? it's about sets and manifolds and rings and groups and graphs and trees and Euler circuits and hyper-cubes and tilings. Mathematics is about patterns.

"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." GH Hardy.

• At 7:20 AM, Joe G said…

It's all moot as nested hierarchies do not rely on Cantor's set theory and nested hierarchies depend on what, exactly, is in their sets.