Products You Never Knew Existed

[Gravdigr]

Originally Posted by Happy Monkey

I don't understand. Subtract decimal points?

The infinite number of nines will still be less than one. You'll have to remove the decimal point completely to get to one. As in, a decimal point, then a billion nines is still less than one.

Originally Posted by Happy Monkey

Likewise, no matter how many nines you add to 0.9999..., you will never reach one - unless you add an infinite number of nines.

The number of nines is irrelevant, it'll always be less than one.

Observation: adding more nines does not change the fact that it is less than one, no matter how many you add.

[Happy Monkey]

A billion nines is less thamn one. Infinite nines is equal to one.

The number of nines is irrelevant, unless it's an infinite number. Then it's one. No matter how you look at it mathematically.

1/9 = .1111...
9/9 = .9999... = 1

10x = 9.9999...
x = .9999...
9x = 9
x = 1

Originally Posted by wikipedia

• Some students interpret "0.999..." (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".[37]

This seems to be what you are doing.

[ZenGum]

This may never die.

Approaching the problem for another angle.

1 - 0.9r = ?

either = 0 , or = 0.000r1 (that is, an infinite string of zeros with a one at the end. Which I know makes no sense, but this is maths so never mind)

So what does happen if you divide one by zero?

either 1 / 0 = 0
or
1 / 0 = 0.0r1

My intuition is the latter. Which makes me think that 0.0r1 is a coherent concept, and that it is the difference between 0.9r and 1.

Yes, I just divided by zero on the 29th of February, 2012. WTF am I doing?

[Happy Monkey]

Originally Posted by ZenGum

This may never die.

Approaching the problem for another angle.

1 - 0.9r = ?

either = 0 , or = 0.000r1 (that is, an infinite string of zeros with a one at the end. Which I know makes no sense, but this is maths so never mind)

Zero. If there are infinite zeros, there is no end for there to be a one on.

So what does happen if you divide one by zero?

either 1 / 0 = 0
or
1 / 0 = 0.0r1

My intuition is the latter. Which makes me think that 0.0r1 is a coherent concept, and that it is the difference between 0.9r and 1.

Neither. Are you claiming that 0.0r1 x 0 = 1?

Yes, I just divided by zero on the 29th of February, 2012. WTF am I doing?

As you seem to be aware, division by zero is not possible.

[ZenGum]

So what does happen if you divide one by zero?

either 1 / 0 = 0
or
1 / 0 = 0.0r1

My intuition is the latter. Which makes me think that 0.0r1 is a coherent concept, and that it is the difference between 0.9r and 1.

Total brain fart.
I was thinking about dividing by infinity.

Ahem...

So what does happen if you divide one by infinity?

either 1 / inf = 0
or
1 / inf = 0.0r1

My intuition is the latter. Which makes me think that 0.0r1 is a coherent concept, and that it is the difference between 0.9r and 1.

And in response to

unless it's an infinite number

I think this is an impossible construction.
Infinity is not a number. It is a concept defined in terms of numbers but it is not itself a number. No number is infinite.

[Happy Monkey]

Right. Infinity is not a number. So all examples of a billion nines, or a billion zeros followed by one, do not apply.

So if 0.0 is followed by infinite zeros, you can't put a one after it. There is no "after it". 0.0r1 = 0.0r = 0.

Therefore 1 - 0.9r = 0.0r = 0.
One divided by infinity = 0.0r = 0.

[classicman]

Originally Posted by Happy Monkey

So all examples of a bazillion nines, or a bazillion zeros followed by one, do not apply.

ftfy
Ok, thats all I got.

[ZenGum]

I'm not convinced by that.

We define i as the square root of minus one, despite the fact that there is no number which can be multiplied by itself to produce minus one.

I see no reason to not define "infinitesimality" as 0.0recurring01.

Mathematicians just make shit up all the time, but they call it "stipulating". Why can't I? :p

[Happy Monkey]

Let's do some math with 0.0r1

10 x 0.0r1 = 0.0r1

(10 x 0.0r1) - (1 x 0.0r1) = (9 x 0.0r1)
0.0r1 - 0.0r1 = ( 9 x 0.0r1)
0 = ( 9 x 0.0r1)
0/9 = 0.0r1
0 = 0.0r1

So even if we stipulated that putting a one "after" infinite zeros was syntactically meaningful, it would still equal zero.

[wolf]

Originally Posted by ZenGum

We define i as the square root of minus one, despite the fact that there is no number which can be multiplied by itself to produce minus one.

That's why it's an imaginary number.

Mathematicians just make shit up all the time, but they call it "stipulating". Why can't I? :p

When you have a PhD in a field no one can understand, you can get away with a lot. Hell, they got the New Math over on us. It's all gravy from that point forward.

[HungLikeJesus]

I'm trying to remember why this is in the Products ... thread. I'm too lazy to go back and search for the origin.

[Happy Monkey]

Originally Posted by HungLikeJesus

I'm trying to remember why this is in the Products ... thread. I'm too lazy to go back and search for the origin.

This.

[BigV]

Originally Posted by HungLikeJesus

I'm trying to remember why this is in the Products ... thread. I'm too lazy to go back and search for the origin.

cause they're timesing some numbers.

[ZenGum]

Originally Posted by BigV

cause they're timesing some numbers.

:Long hard stare:

even by my standards, that was pretty bad.

[kerosene]

Maybe there should be a subforum...or even just a thread for all the mathiness that goes on around here.