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/sci/ - Science & Math

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8847282 No.8847282 [Reply] [Original]

If each and every number can be divided into smaller and smaller fractions *infinitely*, and pi, e, etc. are numbers with infinite decimals, why aren't they rational? Since fractions can be expressed infinitely, this should encompass all of the supposed irrational numbers. There is no reason that they shouldn't.

>> No.8847299

>>8847282

Pi CAN be expressed as an INFINITE ratio, 1/pi. We call it irrational because you can't write it out, because it's infinite.

>> No.8847364

>>8847282
>Are irrational numbers bullshit?
No. They are just the completion of Q.
In other words they are all the equivalence classes of Cauchy series in Q.

This means that any Real number can be expressed arbitrarily well by a series of rational numbers.
But this series doesnt necessarily converge.

>> No.8847384

>>8847282
You don't understand the concept of the completion of a space. Yes, you can create a sequence of rationals that gets closer to each irrational with each element, but this doesn't guarantee the element you are approaching is rational.

>> No.8847557
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8847557

>>8847282
how can irrationals be real if reals aren't real

>> No.8847568

>>8847299
Does that mean REAL numbers can't be counted since PI is IRRATIONAL but it's actually REAL since it's a REAL thing you can't have a circle without PI because it's a REAL BIG PROBLEM which means if PI can't be counted because it's REAL then REAL numbers also can't be counted because they're REAL BIG PROBLEMS

>> No.8847604

>>8847282
You don't make sense. Dividing numbers infinitely is not the same as representing a number as a ratio of others.

You can easily prove numbers are irrational by using the fundamental theorem of algebra

>> No.8847683

>>8847557
how do you explain the existence of sqrt(2) then?