Does .9-repeating equal 1?

[chequita guevara]

Originally posted by KrazyHorse


Are you an idiot?

You have to ask?

[chequita guevara]

Originally posted by TCO
This is from grammar school. You little wussie dogs.

No, it's from high school. At first glance, it doesn't seem to make sense. People want to inherently believe in an infinitesimal, but 0.0...1 doesn't exist. It can't exist. 0.9... must be 1, because there is nothing you could add to the number to make it equal to 1.

[TCO]

Originally posted by KrazyHorse
Here's a clever problem I came across the other day:

I have a punch which is very special. If I center it over a point then it removes all the points in the real plane (RXR) which are an irrational distance away from the original point.

How many punches do I need in order to remove the whole real plane?

You are too smart for me. I'll give it a shot though.

Two? Punch once on pi and then once on a point an irrational distance from pi?

[chequita guevara]

That would definitely work.

[KrazyHorse]

No it wouldn't.

You're trying to remove the whole real plane, not the real line.

The initial point being pi is a red herring. You can punch once for free on the origin (without loss of generality). Your next punch has to be an irrational distance i from the origin (else it obviously leaves the origin). Again, WLOG it can be along the positive x axis.

However, now look at the vertical line x = i/2

For any i there exists a real j such that sqrt(i*i/4 + j*j) is rational. In particular, take sqrt(ceil(i/2)*ceil(i/2) - i*i/4) for your j. (where ceiling is the least integer greater than i). So, (i/2, j) is a rational distance from (0,0) However, any point along the line x=i/2 is the same distance from (i,0) as it is from (0,0). So, there is at least one point which has not been removed.

[DRoseDARs]

This is the gayest math thread in all of existence.

[DRoseDARs]

I present this thread as proof that the United States' educational system is failing its students: Arguing that .9-repeating is equal to 1...



...the horror.

[SlowwHand]

.999 repeating is just a math geek with a stutter.

[-Jrabbit]

The answer boils down to onesimple phrase, understandable by even the fuzziest of liberal arts and music majors:

Q: Does 0.9 repeating equal 1?
A: Close enough for rock!

[SlowwHand]

Well there you have it, kids.

[Lancer]

No.

That it's even a question just shows how twisted is the world.

[SlowwHand]

Look at who's debating it, for crying out loud.
Guys with polka dot shirts and plaid pants.

[Lancer]

I should try this on the boss. I'm supposed to clock out at midnight but instead I'll clock out at 11:59 and show her a copy of this thread.

[DRoseDARs]

Actually, you should clock out at 11:59:59.999...

[Lancer]

I can't wait around all that long.