.9 (repeating) = 1
Yes, it's true
Monday, January 24, 2005 by thethimble | Discussion: WinCustomize Talk
In math class, we ventured upon something that I would like to show you all:
.9 (repeating) as in .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is actually equal to 1. Not approximately, but ACTUALLY.
Here's the proof:
x = .9 repeating
10x = 9.9 repeating
10x - x = 9.9 repeating - .9 repeating
9x = 9
x = 1
Therefore .9 repeating = x = 1.
I always assumed that a variable cannot stand for two numbers, so this must be true. Have fun pondering
.9 (repeating) as in .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is actually equal to 1. Not approximately, but ACTUALLY.
Here's the proof:
x = .9 repeating
10x = 9.9 repeating
10x - x = 9.9 repeating - .9 repeating
9x = 9
x = 1
Therefore .9 repeating = x = 1.
I always assumed that a variable cannot stand for two numbers, so this must be true. Have fun pondering
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thethimble
Reply #42 Tuesday, January 25, 2005 9:08 PM
Reply #42 Tuesday, January 25, 2005 9:08 PM
After thinking about this thread all night long I've come up with the conclusion that the doorknob thing is wrong. "The distance between me and the doorknob can always be cut in half." That statement is completely true, except for the fact that when I'm normally traveling toward the doorknob, I don't cut my distance in half. I travel at a near-constant velocity. If I continually cut my distance in half, I would look like a person walking in a strobe light . Here are a couple of examples:
I am 10 meters away from the doorknob
The distance beetween me and the doorknob cuts in half every second
I would never be able to reach the doorknow because:
Original Distance: 10
Next Step: 5
Next Step: 2.5
...
.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000125
The above scenario would make sense if the distance between me and the doorknob was cut in half. I have yet to see a person cut their distance in half while coming towards me .
This scenario is how both you and me approach the doorknob:
Distance to doorknob: 10 meters
Velocity: 2 m/s
Time taken to reach doorknob: 5 Seconds
After 5 seconds, the distance between me and the doorknob would be exactly 0 meters
.
Go Ponder
I've come up with the conclusion that the doorknob thing is wrong. "The distance between me and the doorknob can always be cut in half." That statement is completely true, except for the fact that when I'm normally traveling toward the doorknob, I don't cut my distance in half. I travel at a near-constant velocity. If I continually cut my distance in half, I would look like a person walking in a strobe light . Here are a couple of examples:I am 10 meters away from the doorknob
The distance beetween me and the doorknob cuts in half every second
I would never be able to reach the doorknow because:
Original Distance: 10
Next Step: 5
Next Step: 2.5
...
.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000125
The above scenario would make sense if the distance between me and the doorknob was cut in half. I have yet to see a person cut their distance in half while coming towards me
.This scenario is how both you and me approach the doorknob:
Distance to doorknob: 10 meters
Velocity: 2 m/s
Time taken to reach doorknob: 5 Seconds
After 5 seconds, the distance between me and the doorknob would be exactly 0 meters
.
Go Ponder
thethimble
Reply #43 Tuesday, January 25, 2005 9:10 PM
Reply #43 Tuesday, January 25, 2005 9:10 PM
In response to the ./9/ thing, for all of my purposes, which does not include interstellar travel, ./9/ is equal to one. Heck, let it be .00000000......1 less, but for doing my math homework, it really doesn't matter
Jafo
Reply #44 Tuesday, January 25, 2005 9:13 PM
Reply #44 Tuesday, January 25, 2005 9:13 PM
thethimble...it's a matter of relativity...and conceptual infinity.
In 'theory', since there is an infinite number of 'small distances' between you and the doorknob you can never reach it.....except you can...because infinity is a concept, not a distance.
-OZZY-
Reply #45 Tuesday, January 25, 2005 9:21 PM
Reply #45 Tuesday, January 25, 2005 9:21 PM
infinity is a distance.....i guess....it's a distance that grows bigger with the speed of light.....so you'll never reach the end....or am i wrong...i sometimes wonder what it would look like if there was absolutely nothing...no star, no planets, no universe, just nothing....i just always get dizzy thinking about that, don't know why i do that either, just try it sometime.....
craeonics
Reply #46 Wednesday, January 26, 2005 7:37 AM
Reply #46 Wednesday, January 26, 2005 7:37 AM
Shield you eyes from all light and you will see what absolute nothingness looks like. Rather dark.
AndreasV
Reply #48 Wednesday, January 26, 2005 10:30 AM
No. In logics, AND is *, and OR is + 
Reply #48 Wednesday, January 26, 2005 10:30 AM
| It says time AND money, that means time + money, not time * money, so everything else after that is false. |
craeonics
Reply #49 Wednesday, January 26, 2005 10:52 AM
Reply #49 Wednesday, January 26, 2005 10:52 AM
ozzy: "Dark" is the absence of light. Note the word "absence". Nothingness is black (because there is nothing to emit or reflect light).
-OZZY-
Reply #50 Wednesday, January 26, 2005 10:58 AM
Reply #50 Wednesday, January 26, 2005 10:58 AM
i understand that.....but without light there is no dark, without evil there is
no good, without negative there is no positive...etc...
so that's what i mean there would be no dark....(always fun to have a discussion)
no good, without negative there is no positive...etc...
so that's what i mean there would be no dark....(always fun to have a discussion)
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Reply #41 Tuesday, January 25, 2005 8:04 PM