>>13948617I haven't been part of the discussion and I agree with your sentiment in
>>13939908 that declaring a symbol to represent a number does not bring it into existence. (The Greeks cleverly avoided irrationals, or infinite decimals/fractions, by making statements akin to 'this ratio cannot be expressed in a finite way, because assuming so leads to a contradiction'.)
Infinite sums can be quite definite, thought. For example, the sum of the reciprocals of the powers of two 1/2+1/4+1/8+... converges to 1, as can be seen by cutting a square of area 1 into halves, and one of those halves into two fourths, and one of those fourths into two eights etc. Adding up the areas of all rectangles yields the original square, proving the identity. Similarly, I know Archimedes calculated some infinite series too to find the area between a line and a parabola. I'm not saying this particular (or any) infinite sum that converges to "pi" is of the same nature, but infinite sums can't be dismissed altogether.
You say that pi is nothing but an expression and their attempts don't seem to have disproven that yet, but I think it's only fair if you could answer your own challenge: can you exhibit a definite number that is more than just an expression?
