f we agree that there are eternal mathematical truths then the question arises how many are there..the answer will be either some finite number or infinite.
A sum such as 1+1=2 is an eternal truth and there are an infinite number of such sums.
If you study the diagram closely, it may take a while to appreciate it but there are 27 possible trinary permutations over 3 places.:
Look closely:there are 27 geometric features of the cube: 8 corners, 12 edges, 6 faces and 1 center, 27 in total.
Of the 27 permutations there are exactly 8 with no 'dot' (in this case). There are exactly 12 permutations with one dot and there are exactly 6 with 2 dots. Then there is only one with all dots.
So we can see that interestingly there is a direct one to one correlation between the 27 permutations and the 27 geometric features of the cube.
Now the same relationship holds true for each of the infinite series of n-dimensional hypercubes with a corresponding set of trinary permutations.
There already we have 2 examples of infinite numbers of unchanging mathematical truths.
Do you have a different view on this? If we agree that there are eternal mathematical truths then the question arises how many are there..the answer will be either some finite number or infinite.
A sum such as 1+1=2 is an eternal truth and there are an infinite number of such sums.
If you study the diagram closely, it may take a while to appreciate it but there are 27 possible trinary permutations over 3 places.
Look closely: there are 27 geometric features of the cube: 8 corners, 12 edges, 6 faces and 1 center, 27 in total.
Of the 27 permutations there are exactly 8 with no 'dot' (in this case). There are exactly 12 permutations with one dot and there are exactly 6 with 2 dots. Then there is only one with all dots.
So we can see that interestingly there is a direct one to one correlation between the 27 permutations and the 27 geometric features of the cube.
Now the same relationship holds true for each of the infinite series of n-dimensional hypercubes with a corresponding set of trinary permutations.
There already we have 2 examples of infinite numbers of unchanging mathematical truths.
Do you have a different view on this?