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The correct question is not :

How to decide if an axiom is right or wrong ...

but :

Of what "domain" (of discourse or of reality) is this axiom true ?

Modern mathematics, after Georg Cantor, has found "domains" (infinite colelctions or sets) where it is not true that

the whole [is] greater than the part

for a "suitable" interpretation of greater than.

As was already known to Galileo (see Galileo's paradox) we can associate to each natural number n its double : 2n.

Thus, if we use this "procedure" to count the objecst in a colelctioncollection, we can roughly satsay that the colelctioncollection of natural numbers has the "same number" of elements as the colelctioncollection of "even* numbereven numbers.

This result show us that, for infinite collection, we can roughly say that

the whole is not always "greater than" a proper part of it.

The correct question is not :

How to decide if an axiom is right or wrong ...

but :

Of what "domain" (of discourse or of reality) is this axiom true ?

Modern mathematics, after Georg Cantor, has found "domains" (infinite colelctions or sets) where it is not true that

the whole [is] greater than the part

for a "suitable" interpretation of greater than.

As was already known to Galileo (see Galileo's paradox we can associate to each natural number n its double : 2n.

Thus, if we use this "procedure" to count the objecst in a colelction, we can roughly sat that the colelction of natural numbers has the "same number" of elements as the colelction of "even* number.

This result show us that, for infinite collection, we can roughly say that

the whole is not "greater than" a proper part of it.

The correct question is not :

How to decide if an axiom is right or wrong ...

but :

Of what "domain" (of discourse or of reality) is this axiom true ?

Modern mathematics, after Georg Cantor, has found "domains" (infinite colelctions or sets) where it is not true that

the whole [is] greater than the part

for a "suitable" interpretation of greater than.

As was already known to Galileo (see Galileo's paradox) we can associate to each natural number n its double : 2n.

Thus, if we use this "procedure" to count the objecst in a collection, we can roughly say that the collection of natural numbers has the "same number" of elements as the collection of even numbers.

This result show us that, for infinite collection, we can roughly say that

the whole is not always "greater than" a proper part of it.

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source | link

The correct question is not :

How to decide if an axiom is right or wrong ...

but :

Of what "domain" (of discourse or of reality) is this axiom true ?

Modern mathematics, after Georg Cantor, has found "domains" (infinite colelctions or sets) where it is not true that

the whole [is] greater than the part

for a "suitable" interpretation of greater than.

As was already known to Galileo (see Galileo's paradox we can associate to each natural number n its double : 2n.

Thus, if we use this "procedure" to count the objecst in a colelction, we can roughly sat that the colelction of natural numbers has the "same number" of elements as the colelction of "even* number.

This result show us that, for infinite collection, we can roughly say that

the whole is not "greater than" a proper part of it.