Not really. Pi is not absolute but rather a floating function calculation that how many decimals determines minute changes in the whole calculation. The use of two decimals behind the dot are only meant to simplify the calculation, which won't end if you tried to do it with the original result. Basically only in calculating things related to Pi mathematicians are dealing in absolutes XD
Not really. Pi is not absolute but rather a floating function calculation that how many decimals determines minute changes in the whole calculation. The use of two decimals behind the dot are only meant to simplify the calculation, which won't end if you tried to do it with the original result. Basically only in calculating things related to Pi mathematicians are dealing in absolutes XD
In any case, you're talking like a computer scientist, not a mathematician. Pi is an irrational number, yes, and a transcendental one at that, but it still corresponds to a SINGLE point on the real number line (or complex plane, if you want to include the other complex numbers). It is a well-defined number, that is, the ratio of a circle's circumference to its diameter. Just because you can't represent it with absolute precision in decimal representation doesn't mean it does not have a specific value.
Cauchy sequences or epsilon-delta proofs can prove rigorously that pi is a constant.
And no, math doesn't care about quantum mechanics and limits on precision (blah blah, nothing is a perfect circle in real life, blah blah it doesn't care). It operates in the realm of pure thought, albeit one that is systematically constructed to eliminate contradictions (and of course, just because something is counter-intuitive or a 'paradox' doesn't mean it's a contradiction). Hence, absolutes.
And, also, mathematical proofs often involve the use of 'absolute' language, with ∀ being a perennial favorite.
In any case, you're talking like a computer scientist, not a mathematician. Pi is an irrational number, yes, and a transcendental one at that, but it still corresponds to a SINGLE point on the real number line (or complex plane, if you want to include the other complex numbers). It is a well-defined number, that is, the ratio of a circle's circumference to its diameter. Just because you can't represent it with absolute precision in decimal representation doesn't mean it does not have a specific value.
Cauchy sequences or epsilon-delta proofs can prove rigorously that pi is a constant.
And no, math doesn't care about quantum mechanics and limits on precision (blah blah, nothing is a perfect circle in real life, blah blah it doesn't care). It operates in the realm of pure thought, albeit one that is systematically constructed to eliminate contradictions (and of course, just because something is counter-intuitive or a 'paradox' doesn't mean it's a contradiction). Hence, absolutes.
And, also, mathematical proofs often involve the use of 'absolute' language, with ∀ being a perennial favorite.
Y AM I LUKING AT MATHEMATICAL DISCUSSIONS IN DANBOORU...
Seriously, when I first saw the claim "PI is not absolute" I thought we were dealing with non-Euclidean geometry or something.
Y AM I LUKING AT MATHEMATICAL DISCUSSIONS IN DANBOORU...
Seriously, when I first saw the claim "PI is not absolute" I thought we were dealing with non-Euclidean geometry or something.
It's Nnescio. Only them and a few others has the ability to discuss on an educated topic in such manner. I would too if it weren't for my sheer laziness and lack of interest towards the subject in question.