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Phrak
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Infinitesimals and "Infini-tesa-tesimals"
Positive infinitesimals are defined as greater than zero, and less than 1/n, where n is any number 1,2,3... The set of negative infinitesimals is the same, but where negative infinitesimals are less than zero and greater than 1/-n.
Infinities are the reciprocal of infinitesimals.
Call the set of real numbers A0. Call the set of infinitesimals A-1. Call the set of infinities A1.
Now, I'd like to have more sets with elements smaller than A-1 but greater than zero, and sets with elements larger than A1 for the positive elements of each set:-
The set of sets being …, A-2, A-1, A0, A1 , A2, … .There’s an immediate problem as there isn’t any room left between zero and A-1 to fit A-2.
Can this be resolved and a consistent arithmetric with the operators (+,-,*,/) be obtained?
Positive infinitesimals are defined as greater than zero, and less than 1/n, where n is any number 1,2,3... The set of negative infinitesimals is the same, but where negative infinitesimals are less than zero and greater than 1/-n.
Infinities are the reciprocal of infinitesimals.
Call the set of real numbers A0. Call the set of infinitesimals A-1. Call the set of infinities A1.
Now, I'd like to have more sets with elements smaller than A-1 but greater than zero, and sets with elements larger than A1 for the positive elements of each set:-
The set of sets being …, A-2, A-1, A0, A1 , A2, … .There’s an immediate problem as there isn’t any room left between zero and A-1 to fit A-2.
Can this be resolved and a consistent arithmetric with the operators (+,-,*,/) be obtained?
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