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A countable set is defined as one whose elements can be put into one-to-one correspondence with elements of the set of counting numbers or some subset of it. A countable set can be infinite: for example all even numbers.
This raises the strange concept where a subset (positive even numbers) has the same cardinality as all counting numbers - which should be a set that is twice as large! Even more confusingly (perhaps) is the fact that the set of all rational numbers also has the same cardinality as the set of counting numbers. You need to go to the set of irrationals or bigger before you get to uncountable sets.
So you have the weird situation in which there are more irrationals between 0 and 1 than there are rationals between from 0 and infinity (if infinity can be treated as a value)!
There is a minority definition of countable which means containing a finite number of elements as opposed to uncountable meaning infinitely many elements. However, these definitions are essentially the same as the finite sets and infinite sets and so there is little point in using them.
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Is cups countable or uncountable?
uncountable
Is few countable or uncountable?
few is countable
Is soap a countable or uncountable noun?
countable
Is daytime countable or uncountable?
The noun 'daytime' is an uncountable noun.
Is Sheet a countable or uncountable noun?
The noun sheet is a countable noun. The plural form is sheets.
Is the set of all irrational number countable?
No, it is uncountable. The set of real numbers is uncountable and the set of rational numbers is countable, since the set of real numbers is simply the union of both, it follows that the set of irrational numbers must also be uncountable. (The union of two countable sets is countable.)
Is transport an uncountable or countable noun?
Transport is both countable and uncountable as a noun.
Is marmalade countable or uncountable?
countable
Is Cereal countable or uncountable?
Uncountable
Is cups countable or uncountable?
uncountable
Is legislation countable or uncountable?
uncountable
How prove that the set of irrational numbers are uncountable?
Proof By Contradiction:Claim: R\Q = Set of irrationals is countable.Then R = Q union (R\Q)Since Q is countable, and R\Q is countable (by claim), R is countable because the union of countable sets is countable.But this is a contradiction since R is uncountable (Cantor's Diagonal Argument).Thus, R\Q is uncountable.
Is painting countable or uncountable?
The gerund painting is a countable noun, as in "There are 12 paintings in this room."
Is few countable or uncountable?
few is countable
Is soap a countable or uncountable noun?
countable
Is mirror countable or uncountable noun?
Countable
Is steel a countable or uncountable noun?
The noun 'steel' is an uncountable (mass) noun, a word for a substance.
