Are there errors in math?

justified · 06-15-2005, 06:33 PM

My math teacher said that .999~ = 1. and showed this proof.
x = .999~ multiply both sides by 10.
10x = 9.999~ subtract x from the left and .999~ from the right.
9x = 9 divide both sides by 9.
x = 1.
That is the proof. I was wondering if there is something wrong with it. It appears to be correct. I think that it is correct, and wanted to know what you think.

pikea · 06-15-2005, 06:38 PM

yeah there are errors in math but gosh that looks confusing

NeverAlone2820 · 06-15-2005, 06:56 PM

Hmm to me step two looks wrong...

HeavenBound · 06-15-2005, 10:22 PM

I think it does too

w.e.g. · 06-16-2005, 05:44 AM

step 2 is wrong because x and .99999aren;'t shown to be equal

justified · 06-16-2005, 08:42 AM

x and .999~ are shown to be equal in the first line.

NeverAlone2820 · 06-16-2005, 11:04 AM

weg, its .999... But yeh i don't see how thats right...

06-16-2005, 11:15 AM

i've been stumping math teachers/students with that one for years

the "problem" with the equation is that .999~ isn't a real number, as it never terminates... so the representation is 100% theoretical.... you then multiply that theoretical number by a real number *10* and assume that the answer is then a part-real part-theoretical number *9.999~*... then you subtract the theoretical part of the number *.999~* and you're only left with the real part of the number

the logical fault is that a real number multiplied by a theoretical number doesn't equal a hybrid... it equals a theoretical number... so the end result *1* would STILL be a theoretical number..... and .999~ DOES = 1... theoretically

justified · 06-16-2005, 03:01 PM

you can show .111~, .222~, .333~... .999~ in fraction form. .111~ = 1/9, .222~ =2/9, .333~ = 3/9... so then it could can be concluded that .999~ =9/9 = 1. Is that not correct.

nvan91 · 06-16-2005, 11:59 PM

The simplest discernable error in that equation is that in order to follow standard mathematical rules you are not allowed to add or subtract opposite sides of an equation. If 18=6x3 and you subtract 2 from each side then apparrently 16=4x3 or 6x1 or 5x2. So yeah your teacher's rationale is incorrect.

06-15-2005, 06:33 PM	#1
justified justified Edit Prophet/Prophetess	Are there errors in math? My math teacher said that .999~ = 1. and showed this proof. x = .999~ multiply both sides by 10. 10x = 9.999~ subtract x from the left and .999~ from the right. 9x = 9 divide both sides by 9. x = 1. That is the proof. I was wondering if there is something wrong with it. It appears to be correct. I think that it is correct, and wanted to know what you think.
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06-15-2005, 06:38 PM	#2
pikea pikea Edit Disciple	yeah there are errors in math but gosh that looks confusing Last edited by pikea; 06-15-2005 at 08:25 PM.. Reason: oopsy?? :)
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06-15-2005, 06:56 PM	#3
NeverAlone2820 NeverAlone2820 Edit Prophet/Prophetess	Hmm to me step two looks wrong... __________________ Heroes are made when you make a choice 1 in 12 teens attempt suicide. 40% of teens are cutters. 48% are sexually active. 1 in 10 fifteen year olds have already gone through at least one divorce in their family. 29 people die every 30 seconds. *&& all of us just sit back* and watch it happen. This is our problem.** So let's wake up and change the world - our time is now
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06-15-2005, 10:22 PM	#4
HeavenBound HeavenBound Edit Prophet/Prophetess	I think it does too __________________ "We have just enough Religion to make us HATE, but not enough to make us LOVE one Another..." -Jonathan Swift Who could hate a Man, who thought about YOU on the Cross?
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06-16-2005, 05:44 AM	#5
w.e.g. w.e.g. Edit Prophet/Prophetess	step 2 is wrong because x and .99999aren;'t shown to be equal __________________ There is no luck only faith. CAP'N WILLY
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06-16-2005, 08:42 AM	#6
justified justified Edit Prophet/Prophetess	x and .999~ are shown to be equal in the first line.
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06-16-2005, 11:04 AM	#7
NeverAlone2820 NeverAlone2820 Edit Prophet/Prophetess	weg, its .999... But yeh i don't see how thats right... __________________ Heroes are made when you make a choice 1 in 12 teens attempt suicide. 40% of teens are cutters. 48% are sexually active. 1 in 10 fifteen year olds have already gone through at least one divorce in their family. 29 people die every 30 seconds. *&& all of us just sit back* and watch it happen. This is our problem.** So let's wake up and change the world - our time is now
Status: Offline

06-16-2005, 11:15 AM	#8
Gobo Gobo Edit Guest	i've been stumping math teachers/students with that one for years the "problem" with the equation is that .999~ isn't a real number, as it never terminates... so the representation is 100% theoretical.... you then multiply that theoretical number by a real number 10 and assume that the answer is then a part-real part-theoretical number 9.999~... then you subtract the theoretical part of the number .999~ and you're only left with the real part of the number the logical fault is that a real number multiplied by a theoretical number doesn't equal a hybrid... it equals a theoretical number... so the end result 1 would STILL be a theoretical number..... and .999~ DOES = 1... theoretically

06-16-2005, 03:01 PM	#9
justified justified Edit Prophet/Prophetess	you can show .111~, .222~, .333~... .999~ in fraction form. .111~ = 1/9, .222~ =2/9, .333~ = 3/9... so then it could can be concluded that .999~ =9/9 = 1. Is that not correct.
Status: Offline

06-16-2005, 11:59 PM	#10
nvan91 nvan91 Edit AY! Newbie	The simplest discernable error in that equation is that in order to follow standard mathematical rules you are not allowed to add or subtract opposite sides of an equation. If 18=6x3 and you subtract 2 from each side then apparrently 16=4x3 or 6x1 or 5x2. So yeah your teacher's rationale is incorrect.
Status: Offline