thethimble thethimble

.9 (repeating) = 1

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.9 (repeating) = 1

Yes, it's true

from WinCustomize Forums
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
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Reply #26 from WinCustomize Forums Top
OK, so I printed out this forum, and showed it to my teacher. Basically, all she said is that you guys are right, and you guys are wrong. She said that "./9/ is a number which cannot be used in math, simply because it goes on forever. No matter how many nines you add to the number, you can still add more. Because of this concept, ./9/ must be equal to 1 because of the fact that ./9/ cannot be logically expressed." After I scratched my head, she clarified. "Lets say my current location on a number line is 1. My destination is ./9/. No matter how small of a step I take towards ./9/, im already too far. The smallest step I can take is 0, but that would leave me at 1. Hence, ./9/ must be equal to one." This clarified it a little, and my final conclusion (unless convinced otherwise) is that ./9/ = 1.
Reply #27 from WinCustomize Forums Top

She's wrong.

0.9999' is not 1.0.

Both are concepts.

The latter is the concept of 'unity' [ONE]

The former is the concept of the largest number imaginable that is LESS than ONE.

By definition, the former is LESS than the latter.

Never make the mistake of blaming mathematics for being unable to distinguish between the two.  The fault lies with the observer and his/her inability to conceptualize.

Infinity is a 'concept'.  [Half of infinity is also a concept...it just so happens to be the same number.]

Get your head around this one....

0.99999' is that infinitesimally smaller number than 1.0

0.00000' [with a '1' on the end IF you could somehow reach infinity] is the amount by which it is less than 1.0

Therefore... 0.99999' + 0.00000' = 1

The 'error' arises when you 'think' that means 0.99999' + 0 = 1

Infinitely-recurring decimals, Infinity, Zero, etc are conceptual absolutes.

Just like 'pregnant' is an absolute....there is no 'more' or 'less', just as there is no more or less 'dead'....

Oh, yeah....another pet peeve......'Midnight' is an absolute....you CANNOT have 'half past Midnight'.

You CAN have 'half past 12', but if anything 'half past Midnight' would be 'Midday'....

Galactic Civilizations III
Reply #28 from WinCustomize Forums Top
Wait...I'm not getting the doorknob thing..

Are you saying that because no matter how small something is you can cut it in half..well..
Half of zero is zero, right?

So, if there's zero distance between you and doorknob, then you touch..


By the way...anyone know the proof for 1 = 2?
Reply #29 from WinCustomize Forums Top
I'm reaching for the doorknob, right now.
Reply #30 from WinCustomize Forums Top
The doorknob thing isn't something I could explain well, it has to do with atoms and stuff, which are microscopic even compared to cells. Still kinda annoying to think about though

You can work with .9 or any other repeating decimal easy enough by rounding or replacing it with a variable. Rounding it to 1 would work good enough for the most part, but to be completely accurate you'd have to just simplify it.
Reply #31 from WinCustomize Forums Top
Hear, hear, J-man.

As for the atoms thing, don't even try to imagine that. At an atomic level (as the theory goes), there is no such thing as "solid mass", just overlapping fields of vibrations with fuzzy boundaries, which can portray both partical and wave behaviour (grave simplification).
Reply #32 from WinCustomize Forums Top
This reminds me of something else I heard once... No 2 objects will ever touch, technically. If an object continues to cut it's distance from another object in half, it can, in theory continually move closer and closer to that object for eternity and never touch it.

This is philosophical, not mathematical. If 2 objects are moving towards eachother, they will do this probably at a constant speed (or, even with an acceleration!), so they will touch each-other. If you halve the distance, you also need to either
a) halve the speed
b) halve the time
If you halve the speed, the speed will go eventually towards 0 (infinitely small).
If you halve the time, you will also go to 0 -time (not moving on in timespace).
So basically, you are changing 2 constant things (speed, time) for an infinite state, in which we can't tell or do nothing. It's pure philosophical.
Reply #33 from WinCustomize Forums Top
By the way...anyone know the proof for 1 = 2?


One does not equal two.

a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1



There's a problem though.


You are dividing each side of the equation by 0. That is a big time no-no.

a = b
multiply both sides by a
a^2 = a*b
subtract b^2 from both sides
a^2-b^2 = a*b-b^2
apply the distributive law to both sides
(a+b)(a-b) = b(a-b)
divide both sides by (a-b)
(a+b) = b
substitute all a's for b's (remember, if a = b you can do this)
a+a = a
regroup the two a's in the left side, and rename it 2a
2a = a
divide both sides by a
2 = 1

The italicized and underlined part is where you are dividing by zero. If the first line of the proof is correct (a=b) then a-b is zero.
Reply #34 from WinCustomize Forums Top
im lost
Reply #35 from WinCustomize Forums Top
Has anyone heard the proof that girls are evil?

We all know that Girls require two things: time and money

So: Girls = Time x Money

We also know that time is money, i.e: Time = Money

Therefore: Girls = Money x Money = (Money)^2

And everyone knows that Money is the root of all evil, ie: Money = sqrt(evil)

Making: Girls = sqrt((evil)^2)

Therefore we are forced to conclude that:

Girls = evil
Reply #36 from WinCustomize Forums Top
I knew that the 1 = 2 proof isn't accurate, and kind of a joke, but, it's still amusing..

I'm also aware of what atoms are and whatnot, but that still doesn't explain why you can't touch the doorknob..
I mean...It explains that you can't physically touch it, but just because you can't physically touch atom to atom doesn't mean you can't manipulate things..
Reply #37 from WinCustomize Forums Top
As for the atoms thing, don't even try to imagine that. At an atomic level (as the theory goes), there is no such thing as "solid mass", just overlapping fields of vibrations with fuzzy boundaries, which can portray both partical and wave behaviour (grave simplification).



Does this refer to gravity and the bonding mass of one object to another?

I can technically see my hand pushing the doorknob, but what is happening is that the 'doorknobs' atoms and my 'hands' atoms actually cross boundries. What holds my hand together and what holds the doorknob together creates a force that allows them to intact (IE push/pull etc)

Right?

So the resistance force is the limit of the boundries crossing that is allowed by physical law.



So, can we mentally control our atoms so that we could walk through walls?
Reply #38 from WinCustomize Forums Top
Girls are evil. No riddle there. Manipulating, deviant, bossy....

oops. Did I say that out loud?
Reply #39 from WinCustomize Forums Top
Has anyone heard the proof that girls are evil?

We all know that Girls require two things: time and money

So: Girls = Time x Money

We also know that time is money, i.e: Time = Money

Therefore: Girls = Money x Money = (Money)^2

And everyone knows that Money is the root of all evil, ie: Money = sqrt(evil)

Making: Girls = sqrt((evil)^2)

Therefore we are forced to conclude that:

Girls = evil

While I won't disagree that we girls are evil, there's a flaw in that "proof."

It says time AND money, that means time + money, not time * money, so everything else after that is false.
Reply #40 from WinCustomize Forums Top
Some one here is three ha'pence short of a farthing...
Reply #41 from WinCustomize Forums Top
The atoms thing I don't get, just what I heard.
Reply #42 from WinCustomize Forums Top
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
Reply #43 from WinCustomize Forums Top
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
Reply #44 from WinCustomize Forums Top

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.

Reply #45 from WinCustomize Forums Top
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.....
Reply #46 from WinCustomize Forums Top
Shield you eyes from all light and you will see what absolute nothingness looks like. Rather dark.
Reply #47 from WinCustomize Forums Top
"dark" also wouldn't exist.....
Reply #48 from WinCustomize Forums Top
It says time AND money, that means time + money, not time * money, so everything else after that is false.
No. In logics, AND is *, and OR is +
Reply #49 from WinCustomize Forums Top
ozzy: "Dark" is the absence of light. Note the word "absence". Nothingness is black (because there is nothing to emit or reflect light).
Reply #50 from WinCustomize Forums Top
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)