Redefining Reality - The Intellectual Implications of Modern Science

that if two lines are approaching each other, they will eventually
intersect. It’s usually thought of in terms of an equivalent
formulation: Consider a line and a point not on that line. One and
only one line can be drawn through the point that will be parallel
to the original line.
from the other four, Euclid’s system would become even more
postulate (the parallel postulate), but it was never found—because
it does not exist.
After mathematicians failed in their attempts to create a direct proof
idea to try an indirect proof. In this method, something is shown to
be true by demonstrating that it can’t be false.
derive a contradiction, that is, any sentence of the form “A and
not A.” Because either A or not A must be true and both cannot
be, the contradiction “A and not A” must be false.
triangles with the same angles but different sizes or the internal
angles of triangles can add to less than 180 degrees. Such statements
seemed as if they were false, but there was never a contradiction
that had to be false.
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