Do Infinite Sets K Have Equal Cardinalities for Permutations and All Functions?

moo5003
Messages
202
Reaction score
0
Is it true that the set of permutations on a infinite set K has the same cardinality as all functions between a infinite set K to itself?
 
Physics news on Phys.org
Did you try to set up a bijection? Or did you try anything to (dis)prove what you're aksing for?
 
To add to what Pere Callahan said: How many permutations are there on K= {a, b}?
How many functions are there from K to K?
(Permutations are one-to-one and onto functions.)
 

Thread 'Roulette wheel physics and probability'

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
View full post »
Thread 'Detail of Diagonalization Lemma'

Thread 'Detail of Diagonalization Lemma'

The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in the second step in the last line, where we have an m-overlined, and we substitute the expression for m. Are we saying that the name of a coded term is the same as the coded term? Thanks in advance.
View full post »

Similar threads

I Does the definition of cardinality assume distinguishability?
Replies
9
Views
1K
I Add an exponential number of elements, what will be the final cardinality?
Replies
16
Views
2K
MHB Upper and lower bounds for the cardinalities
Replies
17
Views
2K
I Cardinality of non-measurable sets
Replies
7
Views
2K
I Cardinality of the Power Series of an Infinite Set
Replies
19
Views
4K
A Comparing infinite countable sets
Replies
22
Views
2K
I Cardinality of decreasing functions from N to N
Replies
19
Views
3K
MHB One to One Correspondence vs One to One function
Replies
1
Views
3K
I Does one need V not equal to L in order to do Cohen's forcing?
Replies
13
Views
2K
I When does ## { n \choose k } ## represent set of lists?
Replies
20
Views
2K

Hot Threads

Recent Insights

Back
Top