1912 Manuscript Analysis
Problem Definition  Defining the Math Rule
T
HE
M
ATH
R
ULE
FOR
C
HALLENGING
E
INSTEIN
'
S
1912 M
ANUSCRIPT
There are two rules used to evaluate Einstein's 1912 manuscript;
implication
and
equivalence
.
E
QUIVALENCE
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 visaversa. In addition, when
P
is
FALSE
,
Q
is also
FALSE
, and visaversa. 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
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 Spring '11
 Kelly
 Logic, P. Einstein, mathematically incorrect replacement, math rule

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