MHB One to One Correspondence vs One to One function

  • Thread starter Thread starter bigpunz04
  • Start date Start date
  • Tags Tags
    Function
bigpunz04
Messages
4
Reaction score
0
What is the difference between the two?

The topic we are currently reading about is Set Cardinality. There are a couple of definitions listed in the book that seem to define them as different properties of sets. Is there a difference between the two or are they different terms with the same meaning? See below:

Definition 1
The sets A and B have the same cardinality if and only if there is a "one-to-one correspondence" from A to B. When A and B have the same cardinality, we write |A| = |B|

Definition 2
If there is a "one-to-one function" from A to B, the cardinality of A is less than or the same as the cardinality of B and we write |A| <= |B|. Moreover, when |A|<=|B| and A and B have different cardinality, we say that the cardinality of A is less than the cardinality of B and we write |A|<|B|

Thank you!
 
Physics news on Phys.org
One-to-one function is otherwise called an injection. One-to-one correspondence is called a bijection. It is an injection that is also a surjection. I agree that the English names are somewhat confusing.
 
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...
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.
Back
Top