Does a set with a unique element have cardinality 1 or ≤1?

  • Context:
  • Thread starter Thread starter ozkan12
  • Start date Start date
  • Tags Tags
    Cardinality Set
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
6 replies · 3K views
ozkan12
Messages
145
Reaction score
0
Suppose that set A have unique element...Can we say that cardinality(A)=1 or $cardinality(A)\le1$ ? Which one is true ?
 

Discussion

Physics news on Phys.org
ozkan12 said:
Suppose that set A have unique element...Can we say that cardinality(A)=1 or $cardinality(A)\le1$ ? Which one is true ?
Both are true.
 
ozkan12 said:
Suppose that set A have unique element...Can we say that cardinality(A)=1 or $cardinality(A)\le1$ ? Which one is true ?

Hi ozkan12,

For a finite set Cardinality is the number of elements in the set. If $A$ contains only one element its cardinality is $1$. Saying $\mbox{Cardinality}(A)=1$ is more precise than saying $\mbox{Cardinality}(A)\leq 1$ since the former tells $A$ has exactly one element, whereas the latter tells $A$ has one or no elements.
 
First of all, Thank you for your attention...İn your opinion, Which is true ? How both of them is true ?
 
ozkan12 said:
First of all, Thank you for your attention...İn your opinion, Which is true ? How both of them is true ?

You are welcome. This is similar to writing $x=1$. And then saying $x\leq 1$. The $\leq$ sign represents "less than OR equal to". Therefore if $x=1$, it implies that $x\leq 1$ also. In words, $x$ is equal to one and therefore it is also true that $x$ is less than or equal to one.
 
That is, we can say that x=1 is more general than $x\le1$
 
ozkan12 said:
That is, we can say that x=1 is more general than $x\le1$

$x=1$ gives more information as it tells us specifically that $x=1$ whereas $x\leq 1$ gives less information; $x$ can be one or it can be less than one.