Current Events > If pi has infinite digits then a radius and a circumference can never BOTH be...

(+) Yeah! (+)

...real numbers. Yet logically, both of them HAVE to be real, measurable numbers. This has been bothering me all day.

@PiOverlord
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Irrational numbers ARE real numbers.
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It's infinite in the sense that we can't calculate the end without brute forcing the math
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Paragon21XX posted...

Irrational numbers ARE real numbers.

Okay, but do I still have a point if I exclude the word real from my OP? Realistically, both measurements have to end in SOME finite decimal point, dont they?

A real number does not need a terminating decimal representation
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Oh man if irrationals bother you, you should definitely not start thinking about infinitesimals and infinity paradoxes, and how the harmonic series diverges, etc.. Mathematics is a mindfuck.

Seriously if it really bothers you those never ending digits don't mean anything practically. You can do some very high level, precise, calculations with truncated irrationals. In the real world you very quickly get to a point after a few decimal digits where additional ones make no significant difference to your calculation. The numbers are just too small to matter.
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Ic3Bullet posted...

Paragon21XX posted...

Irrational numbers ARE real numbers.

Okay, but do I still have a point if I exclude the word real from my OP? Realistically, both measurements have to end in SOME finite decimal point, dont they?

That's where significant figures come into play when dealing with real-life measurements. The precision of the final result is dependent upon the number of digits the measurement tool being used can possibly return. If the measured radius has three digits (122, 12.2, 1.22, 0.122, etc), then the final answer will only have 3 digits as well (767, 76.7, 7.67, 0.767, etc).
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Circles in real life have rational radii and circumferences. The limitations of the physical world mean there are only so many atoms that can be used to create a circle.

Math doesn't care about that. Mathematical circles are perfect, and pi is irrational along with at least one of the circumference or radius.
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Frostshock posted...

Circles in real life have rational radii and circumferences. The limitations of the physical world mean there are only so many atoms that can be used to create a circle.

Math doesn't care about that. Mathematical circles are perfect, and pi is irrational along with at least one of the circumference or radius.

To fit the missing piece that wasn't explicitly stated: You have never seen a straight line or perfect circle in your life, and never will. But if you could, then you'd need an infinitely precise measuring tool before you start worrying about multiplying the diameter times the exact value of pi and comparing the irrational answer to an also infinitely precise measurement of the circumference.
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Wanna know something neat? There's an amount of distance so small that you can't go any smaller, thus atoms just teleport to the next smallest distance possible. So really, a number like pi could infinite but in reality would have to have a finite point
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nexigrams posted...

Oh man if irrationals bother you, you should definitely not start thinking about infinitesimals and infinity paradoxes, and how the harmonic series diverges, etc.. Mathematics is a mindfuck.

Seriously if it really bothers you those never ending digits don't mean anything practically. You can do some very high level, precise, calculations with truncated irrationals. In the real world you very quickly get to a point after a few decimal digits where additional ones make no significant difference to your calculation. The numbers are just too small to matter.

Well after I read post #4 it all suddenly made sense to me for some reason.... If I multiply 9 by .3333~ Ill never get a number with a finite decimal place. But that doesnt change the fact 3 is still 1/3 of 9 and .33333~ doesnt have to have a finite ending in order for that to be true.

Im actually a pretty mathematically-minded guy, despite my ignorance of terminology and stuff that I displayed in this topic. If I practiced, I have the potential to be a math wizard. I was always one of the smartest people in every math class I ever took.

Infinity and the universe = rekt
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Having infinite decimals isn't what makes pi irrational. As you've just noted, 1/3 is rational and has infinite 3s. Irrational numbers have infinite, non-repeating decimals.
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