.. because that is where you are allowed to challenge some biblical stories of the math without the fear of expulsion from the elite clubs.
Most of math history is stellar, studded with great works of geniuses, but some results were sanctified and prohibited for questioning due to various forces that were active during the times.
Application of regular logic such as comparison, mapping, listing, diagonals, uniqueness - all are the rules that were bred in the realms of finiteness and physical world. You can't use these things to prove some theories about things are not finite.
I'm aware that I'm ignorant of many things, just like anyone else on this Earth. Some are less ignorant and some are more.
Could you be kind enough to explain the phrase "set of all integers" when the word all can not apply to an unbounded quantity? I think the word all is used loosely to extend it's meaning as used for finite sets, to a non-existent, unbounded set. For example, things such as all Americans, all particles in universe have a meaning because they have a boundary criterion. What is all integers?
I think one need to first define the realm of applicability or domain for the concepts such as comparison, 1-to-1 mapping, listing, diagonals, uniqueness, all etc.
.. because that is where you are allowed to challenge some biblical stories of the math without the fear of expulsion from the elite clubs.
Most of math history is stellar, studded with great works of geniuses, but some results were sanctified and prohibited for questioning due to various forces that were active during the times.
Application of regular logic such as comparison, mapping, listing, diagonals, uniqueness - all are the rules that were bred in the realms of finiteness and physical world. You can't use these things to prove some theories about things are not finite.
This isn't iconoclasm, it's ignorance.
I'm aware that I'm ignorant of many things, just like anyone else on this Earth. Some are less ignorant and some are more.
Could you be kind enough to explain the phrase "set of all integers" when the word all can not apply to an unbounded quantity? I think the word all is used loosely to extend it's meaning as used for finite sets, to a non-existent, unbounded set. For example, things such as all Americans, all particles in universe have a meaning because they have a boundary criterion. What is all integers?
I think one need to first define the realm of applicability or domain for the concepts such as comparison, 1-to-1 mapping, listing, diagonals, uniqueness, all etc.