.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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joeKnowledge
Reply #22 Monday, January 24, 2005 4:58 PM
Reply #22 Monday, January 24, 2005 4:58 PM
crea, so what your saying is that if I split something 3 ways and then put it back together its not whole?
so 3 thirds or 3/3 is not 1
1/3 + 1/3 + 1/3 = 0.999999999999?
even as 1 split 3 ways is .3333333?
See you guys, I knew 1 + 1 = 3!!!
joeKnowledge head hurts now that math does not make sense anymore
so 3 thirds or 3/3 is not 1
1/3 + 1/3 + 1/3 = 0.999999999999?
even as 1 split 3 ways is .3333333?
See you guys, I knew 1 + 1 = 3!!!
joeKnowledge head hurts now that math does not make sense anymore
joeKnowledge
Reply #23 Monday, January 24, 2005 5:04 PM
Damn... How does that work with living Cells? While most split, some merge to form new life. Wouldn't these 2 object have to touch in order to create?
You know, this is why I love math. Its the God science. Just when it means this, it can also mean that as well.
If 2 objects can never tough then what make the reaction when one object hits the other? What makes the force? Gravity? Mass?
Reply #23 Monday, January 24, 2005 5:04 PM
| 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. |
Damn... How does that work with living Cells? While most split, some merge to form new life. Wouldn't these 2 object have to touch in order to create?
You know, this is why I love math. Its the God science. Just when it means this, it can also mean that as well.
If 2 objects can never tough then what make the reaction when one object hits the other? What makes the force? Gravity? Mass?
craeonics
Reply #24 Monday, January 24, 2005 5:29 PM
Reply #24 Monday, January 24, 2005 5:29 PM
joe: No, what I'm saying is that 1/3 is unequal to 0.3, 0.33, 0.333 and so on. That's just an approximation used in calculator displays and such. You can get really close (infinitely close) if you keep adding 3's at the end of the number, but it will never be exactly 1/3.
thethimble
Reply #25 Monday, January 24, 2005 5:38 PM
Reply #25 Monday, January 24, 2005 5:38 PM
I love the doorknob thing by the way. It makes your head hurt
thethimble
Reply #26 Monday, January 24, 2005 5:45 PM
Reply #26 Monday, January 24, 2005 5:45 PM
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.
Jafo
Reply #27 Monday, January 24, 2005 6:39 PM
Reply #27 Monday, January 24, 2005 6:39 PM
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'....
GreatSilverWyrm
Reply #28 Monday, January 24, 2005 10:03 PM
Reply #28 Monday, January 24, 2005 10:03 PM
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?
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?
Sleeping Dragon
Reply #29 Monday, January 24, 2005 10:19 PM
Reply #29 Monday, January 24, 2005 10:19 PM
I'm reaching for the doorknob, right now. 
horiz0n
Reply #30 Tuesday, January 25, 2005 3:25 AM
Reply #30 Tuesday, January 25, 2005 3:25 AM
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.
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.
craeonics
Reply #31 Tuesday, January 25, 2005 7:36 AM
Reply #31 Tuesday, January 25, 2005 7:36 AM
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).
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).
AndreasV
Reply #32 Tuesday, January 25, 2005 9:14 AM
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
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 #32 Tuesday, January 25, 2005 9:14 AM
| 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
halve the timeIf 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.
_DrDrrae_
Reply #33 Tuesday, January 25, 2005 9:55 AM
One does not equal two.
a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+(a- = b(a-
(a+ = 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+(a- = b(a-
divide both sides by (a-
(a+ = 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= then a-b is zero.
Reply #33 Tuesday, January 25, 2005 9:55 AM
| 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+
(a- = b(a-(a+
= ba+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+
(a- = b(a-divide both sides by (a-
(a+
= bsubstitute 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=
then a-b is zero.
im lost
bootasven
Reply #35 Tuesday, January 25, 2005 1:49 PM
Reply #35 Tuesday, January 25, 2005 1:49 PM
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
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
GreatSilverWyrm
Reply #36 Tuesday, January 25, 2005 3:11 PM
Reply #36 Tuesday, January 25, 2005 3:11 PM
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..
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..
joeKnowledge
Reply #37 Tuesday, January 25, 2005 3:35 PM
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 #37 Tuesday, January 25, 2005 3:35 PM
| 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?
Sleeping Dragon
Reply #38 Tuesday, January 25, 2005 6:49 PM
Reply #38 Tuesday, January 25, 2005 6:49 PM
Girls are evil. No riddle there. Manipulating, deviant, bossy....
oops. Did I say that out loud?
oops. Did I say that out loud?
Bebi Bulma
Reply #39 Tuesday, January 25, 2005 7:04 PM
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 #39 Tuesday, January 25, 2005 7:04 PM
| 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.
Fuzzy Logic
Reply #40 Tuesday, January 25, 2005 7:12 PM
Reply #40 Tuesday, January 25, 2005 7:12 PM
Some one here is three ha'pence short of a farthing...
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Reply #21 Monday, January 24, 2005 3:26 PM
In effect it would be almost better to look at it like....
1/3 = .333333 repeating
2/3 = .666667
3/3 = 1
However you just explained "infinity" better than I was able to. The integer itself goes on infinetly, but the number isn't infinity, no number can define infinity.
"No 2 objects will ever touch, technically."
You win the prize for the "how can I reach the doorknob" question.