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One way is Cantor's diagonal argument. See link.

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11y ago

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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.


How do you show irrational number r uncountable?

To show that the set of irrational numbers is uncountable, you can use Cantor's diagonal argument. First, assume that the set of irrational numbers is countable and list them in a sequence. By constructing a new number that differs from each listed irrational number at a specific decimal place, you can demonstrate that this new number is also irrational and not in the original list, leading to a contradiction. Thus, the set of irrational numbers must be uncountable.


Is set R of real numbers is countable set or not?

It is uncountable, because it contains infinite amount of numbers


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Transport is both countable and uncountable as a noun.


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The noun 'daytime' is an uncountable noun.


Is steel a countable or uncountable noun?

The noun 'steel' is an uncountable (mass) noun, a word for a substance.


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The word 'violence' is an uncountable noun.


Is health countable or uncountable?

The noun 'health' is an uncountable noun, a word for a condition.


Is bun countable or uncountable?

"Bun" can be both countable and uncountable. For example, you can say "I bought five buns" or "I would like some bun with my soup."