The article “When experimental mathematics fails” at http://motls.blogspot.com/2012/05/when-experimental-mathematics-fails.html
is actually a good article about mathematics. But, no average web reader can
comprehend it. Its key point is about two numbers however close (even having
500 identical digits after the decimal point) can still be different. In fact,
two numbers can have trillions*trillions*…*trillions identical digits after the
decimal point while they still have different tails. Thus, the following
statement can be practically true.

When a – b = 0, a can still be not equal to b.

Yet, the author of the above-mentioned article failed to
reach this simple logic conclusion. If he has realized this fact, he will
understand a new mathematics.

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