# FAQ: Who Shaves The Barber Question?

## Who created the barber paradox?

The barber paradox, offered by Bertrand Russell, was of the same sort: The only barber in the village declared that he shaved everyone in the village who did not shave himself.

## What is the Russell Barber paradox?

Russell’s paradox is based on examples like this: Consider a group of barbers who shave only those men who do not shave themselves. Suppose there is a barber in this collection who does not shave himself; then by the definition of the collection, he must shave himself. But no barber in the collection can shave himself.

## How do you solve the barber paradox?

Answer: If the barber shaves himself then he is a man on the island who shaves himself hence he, the barber, does not shave himself. If the barber does not shave himself then he is a man on the island who does not shave himself hence he, the barber, shaves him(self).

In the Barber’s Paradox, the condition is “shaves himself”, but the set of all men who shave themselves can’t be constructed, even though the condition seems straightforward enough – because we can’t decide whether the barber should be in or out of the set. Both lead to contradictions.

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## Can the barber shave himself?

The barber is the “one who shaves all those, and those only, who do not shave themselves”. The barber cannot shave himself as he only shaves those who do not shave themselves. Thus, if he shaves himself he ceases to be the barber.

## What are examples of paradox?

Here are some thought-provoking paradox examples:

• Save money by spending it.
• If I know one thing, it’s that I know nothing.
• This is the beginning of the end.
• Deep down, you’re really shallow.
• I’m a compulsive liar.
• “Men work together whether they work together or apart.” – Robert Frost.

## How many types of paradoxes are there?

• ACHILLES AND THE TORTOISE.
• THE BOY OR GIRL PARADOX.
• GALILEO’S PARADOX OF THE INFINITE.

A mathematical paradox is a mathematical conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid. Since both are infinite, they are for both practical and mathematical purposes equal.

## Why does Russell have a paradox?

The significance of Russell’s paradox is that it demonstrates in a simple and convincing way that one cannot both hold that there is meaningful totality of all sets and also allow an unfettered comprehension principle to construct sets that must then belong to that totality.

## Can a set contain itself?

No: it follows from the axiom of regularity that no set can contain itself as an element. (Any set contains itself as a subset, of course.) And that’s a good thing, because sets containing themselves is exactly the kind of thing that leads to Russell’s paradox and other associated problems.