Welcome to free online math help,
Let us study what is mathematics with math helper,
Mathematics can be defined as the construction and exploration of
formal systems. The advantage of this definition is that it emphasizes
the somewhat subtle point that mathematics IS formal -- which is just
another way of saying that it has no NECESSARY relation to anything in
'the real world'.
What all this means is that what is 'true' in mathematics depends
entirely on what axioms you start with, and what rules you use to
combine them. To take your example of 'proving' that the product of
two negatives is positive -- your result is true given the system you
set up, but it may be false in other systems.
I hope the above explanation was useful, now let us study more examples on math forum.
Let us study what is mathematics with math helper,
Mathematics can be defined as the construction and exploration of
formal systems. The advantage of this definition is that it emphasizes
the somewhat subtle point that mathematics IS formal -- which is just
another way of saying that it has no NECESSARY relation to anything in
'the real world'.
What all this means is that what is 'true' in mathematics depends
entirely on what axioms you start with, and what rules you use to
combine them. To take your example of 'proving' that the product of
two negatives is positive -- your result is true given the system you
set up, but it may be false in other systems.
I hope the above explanation was useful, now let us study more examples on math forum.
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