Infinite numbers are strange

StarNamer work

I watched a Youtube video recently and one idea from it has stuck in my head as very strange. I assume everyone's familiar with the idea that if you divide 1 by 7, you get an infinite decimal extending to the right... 1 / 7 = 0.14285714285714285714285714285714... But what if you take that the repeating 6 digit sequence indicated and repeat it infinitely to the right followed by a 3... ...2857142857142857142857142857143 That is clearly an infinity (it has infinitely many digits!), but if you multiply it by 7...

7*3 => 21 => 1 carry 2
7*4 => 28 + carried 2 => 30 => 0 carry 3
7*1 => 7 + carried 3 +> 10 => 0 carry 1
7*7 => 49 + carried 1 => 50 => 0 carry 5
7*5 => 35 + carried 5 => 40 => 0 carry 4
7*8 => 56 + carried 4 => 60 => 0 carry 6
7*2 => 14 + carried 6 => 20 => 0 carry 2
7*4 => 28 + carried 2 => 30 => 0 carry 3...

Ultimately, you get... ...0000000000000000000000000000001 You have an infinite number of zeroes followed by 1, which is just 1. So this infinite number times 7 equals 1, which means it's also 1/7! I'd always been told that multiplying infinity by any number resulted in infinity, but this is clearly an infinite number which when multiplied by 7 is 1!

PIEBALDconsult

Ah, Friday night.

jmaida

:)

"A little time, a little trouble, your better day" Badfinger

jmaida

i don't want to think about it

"A little time, a little trouble, your better day" Badfinger

Kenneth Haugland

As long as it is approximately right, the computer is very happy.

StarNamer work

Kenneth Haugland wrote:

As long as it is approximately right, the computer is very happy.

The accountants aren't! :) Also, which AI are you running which expresses emotion? :)

Lost User

You cannot add a 3 to the end of an infinite number, as that converts it to a finite one.

pkfox

0.14285714285714285714285714285714 If you multiply this by 3 you get very close to Pi

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Kenneth Haugland

Im running Marvin from Hitchhiker's guide to the galaxy. It's useless. Not that anyone cares though :laugh:

Amarnath S

pkfox wrote:

multiply

You meant "add"?

pkfox

I did thanks

In a closed society where everybody's guilty, the only crime is getting caught. In a world of thieves, the only final sin is stupidity. - Hunter S Thompson - RIP

Sander Rossel

And accountants be like "your infinite number has a rounding error and now the books are off!"

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englebart

Don’t let Marvin near your primary computer, it might blue screen itself, permanently!

englebart

I would not consider 1/7 or its decimal equivalent an infinite number. I think technically it is a rational number. Unless you are using a special library, then computers (and especially databases) don’t deal that well with these types of numbers. This is why there are fixed decimals that always round in favor of the bank.

Lost User

Explain the problem? A lot that is infinite to us, can be rounded.

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honey the codewitch

I was told there would be no math.

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TNCaver

So how do you put a 3 at the non-existent 'end' of an infinite sequence?

There are no solutions, only trade-offs.
- Thomas Sowell

A day can really slip by when you're deliberately avoiding what you're supposed to do.
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Chris Maunder

StarNamer@work wrote:

But what if you take that the repeating 6 digit sequence indicated and repeat it infinitely to the right followed by a 3.

But you can't. If you repeat it infinitely that means there's always another digit. When you try and add it to the "end", there's always another digit after that spot, so you're not at the end.

StarNamer@work wrote:

That is clearly an infinity (it has infinitely many digits!),

Not quite. It doesn't mean the result is infinite, just that there's no finite representation in base 10. There are actually many different "infinities". The numbers 1,2,3...is an infinite set. The set of real numbers between 1 and 2 (eg 1.1, 1.01, 1.001 and on and on) is also infinite, and large than the set of integers. One infinity can be bigger than another infinity. Even though they are both infinite. This is why mathematicians never need to do drugs.

cheers Chris Maunder

Daniel Pfeffer

englebart wrote:

This is why there are fixed decimals that always round in favor of the bank.

This is incorrect. Bank accounts use "round to nearest or away", where fractional cents are rounded to the nearest value (up or down). If the residue is exactly 0.5 cents, the number is rounded "away" - up for positive, down for negative. If you are running a credit, this gives you a tiny statistical advantage. If you are running a debit, this gives the bank a tiny statistical advantage. In neither case is this likely to have a measurable effect, unless you aggregate over billions of operations a day.

Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.

Daniel Pfeffer

Infinity is a very tricky concept, and you have misunderstood it. You cannot add anything to the "end" of an infinite sequence - it has no "end". It is as ridiculous as claiming that your password is the last eight digits of Pi.

Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.