Greetings from math forum,
We aren't allowed to introduce additional assumptions (undefined terms
or postulates) or alter them without explicitly stating the new
assumptions. When we do so, we are no longer working in the same
mathematical system. It may be a perfectly valid system, but it isn't
the same one once its rules have been changed, even the slightest bit.
Many mathematical systems - probably all until the last two centuries
or so - were motivated by attempts to describe and explain things in
the real world. examples on free math; At this point, math overlaps
with science, and faith
becomes relevant. Do the undefined terms and postulates of our system
correspond to elements of the real world and their interactions? We
can't know. In all likelihood, they don't correspond exactly, but they
may make a good approximation. read more on online math forum.
We aren't allowed to introduce additional assumptions (undefined terms
or postulates) or alter them without explicitly stating the new
assumptions. When we do so, we are no longer working in the same
mathematical system. It may be a perfectly valid system, but it isn't
the same one once its rules have been changed, even the slightest bit.
Many mathematical systems - probably all until the last two centuries
or so - were motivated by attempts to describe and explain things in
the real world. examples on free math; At this point, math overlaps
with science, and faith
becomes relevant. Do the undefined terms and postulates of our system
correspond to elements of the real world and their interactions? We
can't know. In all likelihood, they don't correspond exactly, but they
may make a good approximation. read more on online math forum.
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