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free math, Definition of math by Bertrand Russell :
In 1901 Bertrand Russell (who once defined mathematics as "the subject
in which we do not know what we are talking about nor whether what we
say is true") discovered the following paradox:
Some sets, such as the set of teacups, are not members of
themselves. Other sets, such as the set of all non-teacups,
are members of themselves. Call the set of all sets which
are not members of themselves S. If S is a member of itself,
then by definition it must not be a member of itself.
Similarly, if S is not a member of itself, then by definition
it must be a member of itself.
This little bump in the road prompted a complete re-examination of the
foundations of mathematics. Godel's discovery was in part a result of
that re-examination.
Now let us go through more examples on online math forum.
free math, Definition of math by Bertrand Russell :
In 1901 Bertrand Russell (who once defined mathematics as "the subject
in which we do not know what we are talking about nor whether what we
say is true") discovered the following paradox:
Some sets, such as the set of teacups, are not members of
themselves. Other sets, such as the set of all non-teacups,
are members of themselves. Call the set of all sets which
are not members of themselves S. If S is a member of itself,
then by definition it must not be a member of itself.
Similarly, if S is not a member of itself, then by definition
it must be a member of itself.
This little bump in the road prompted a complete re-examination of the
foundations of mathematics. Godel's discovery was in part a result of
that re-examination.
Now let us go through more examples on online math forum.
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