Jerzz, the eqn a + b - c = 0 does not need a base/question/story
per say in order to "mean something". By itself, in its raw form if
you may, its just simply 3 variables (a, b and c) amounting to a
value of 0. Perhaps due to the systematic mathematical education of
our Singaporean education, it has lead most of us to attribute
Algebra solely to its APPLICATION without appreciating its
fundamental qualities. To quote an article in Wikipedia regarding
Algebra:
"... While in arithmetic only
numbers and their arithmetical operations (such as +, - , ×, ÷)
occur, in algebra one also uses symbols (such as x and y, or a and
b) to denote numbers. These are called variables. This is useful
because:
* It allows the generalization of arithmetical equations (and
inequalities) to be stated as laws (such as a + b = b + a for all a
and b), and thus is the first step to the systematic study of the
properties of the real number system.
* It allows reference to numbers which are not known. In the
context of a problem, a variable may represent a certain value of
which is uncertain, but may be solved through the formulation and
manipulation of equations.
* It allows the exploration of mathematical relationships between
quantities (such as "if you sell x tickets, then your profit will
be 3x - 10 dollars" )..."
The very basic a + b = c, by itself, may seem "baseless", but in
reality, its simply a representation of fixed numbers of figures,
governed by Algebraic Laws of equality, that through formulation
and manipulation of equations, the solver is able to derive the
deterministic value of a, b and c concerning the mathematical study
of structure, relation and quantity.
For the sake of the argument and the "jist of the joke", since
there isn't any situation/question/problem/story associated with
the eqn, simply manipulation of the figures, as long as its fulfills the Algebraic
Laws of equality, is just fine.
What do I mean by that?
I.e.
Suppose a = b and b = c, then a = c (transitivity of
equality).
Suppose a = a (reflexivity of equality).
Suppose a = b then b = a (symmetry of equality).
Suppose a = b then a + c = b + c for any c (addition property of
equality).
Suppose a = b then ac = bc for any c (multiplication property of
equality).
Suppose two symbols are equal, then one can be substituted for the
other at will (substitution principle).
.
.
.
I can go on and on, but thats besides the point. The fact is that
any Algebraic eqn is forever hold true, as long as
it is constructed and manipulated under the Algebraic Laws of
equality, even though the end result of the manipulation does not
necessarily solve the deterministic values of the eqn.
No doubt it might initially appear "baseless" and IS indeed formed
from nowhere, it does not necessarily make it unsolvable just
because of the word "Suppose".
Now, the fallacy and ultimately the "jist" of the joke is NOT
caused by the word SUPPOSE but rather, the operation of dividing
both sides by (a+b-c) goes directly against the basic Algebraic
Laws of equality! With the "bastardized" end result of 5=4, the
joke proceeds to conclude that 5 does indeed equal to 4, even after
going through a series of meaningful Algebraic manipulation which
ultimately went wrong at the illegal division operation.
And that, my friend, is what makes this all "funny".
Edit: Typos.
