RelativityChallenge - Relativity Book Math Rule (c) 2005

The Math Rule for Challenging Einstein's Relativity Book

There are two rules used to evaluate Appendix 1 of Einstein's Relativity book; implication and equivalence.

Equivalence

There is a mathematical rule that states that two statements, P and Q, are equivalent to each other if when P is TRUE, Q is also TRUE and visa-versa. In addition, when P is FALSE, Q is also FALSE, and visa-versa. When equations are equivalent to each other they can be used as replacements for one other.

Mathematically, equivalence is written as:

P <==> Q

For example, if P is "x+x+x+x=10" and Q is "4x=10", then we can show that P is equivalent to Q. In this case, Q can be used instead of P. If, however, Q is "4x=n", then we can show that Q will be TRUE in cases where P is FALSE. In this case the two statements are not equivalent and it would be a mistake to use Q as a replacement for P.

If we find that Q has been used as a replacement for P, but that Q is not equivalent to P, then we have found an error in the form of a mathematically incorrect replacement.

Implication

This is a mathematical rule that states that given two statements, P and Q, P implies Q if when P is TRUE, Q is also TRUE. When P is FALSE, no statement can be made regarding the validity of Q. In other words, Q can only be used as a replacement for P only in the specific instances where P would have been TRUE.

Mathematically, implication is written as

P ==> Q

For example, if P is "x+x+x+x=10" and Q is "4x=n", then we can show that P implies Q. In this case, Q can be used instead of P as long as P would have itself been TRUE. As a specific example, P implies Q when x=2.5 and n=10. Observe that x=10 and n=40, while resulting in a valid mathematical statement for Q, cannot be used if Q was created as an implication of P because 10+10+10+10=10 is FALSE.

If we find that Q has been used as a replacement for P, in cases where P is FALSE, then we have found an error in the form of a mathematically incorrect replacement.

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