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0.999 (Repeating) is equal to 1

Axonly
Posts: 2,385
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1/31/2016 1:57:48 AM
Posted: 1 year ago
This blows my mind, here is the proof via algebra:
(R means repeating)

(1/9)=0.111(R)

9x(1/9)=0.111(R)

1=0.999(R)

Its so interesting how this works, normally I have limited interest in mathematics, but this takes the cake.

https://en.wikipedia.org...
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Through_the_Monocle
Posts: 1
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1/31/2016 4:59:50 PM
Posted: 1 year ago
Here's another way to understand 0.99 (repeating) is equal to 1:

1/3=0.33 (repeating)
1/3*3=1
0.33 (repeating)*3=0.99 (repeating)=1

There are several other "proofs".
Mhykiel
Posts: 5,993
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1/31/2016 8:16:12 PM
Posted: 1 year ago
http://www.debate.org...

just 1/3 is .3 repeating, the decimal is the real number 1/3.

The reason why it is not an easy to see integer is because the ration 1/3 is applied to a base 10 system. In hexadecimal 1/3 is .5 repeating.

It's a real number. But it's not a real quantity that is infinitely growing large.

It's a common confusion to think a number that expands infinitely is somehow infinite itself. it isn't. It's just one representation of it is with remainder.
famousdebater
Posts: 3,964
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1/31/2016 8:36:42 PM
Posted: 1 year ago
At 1/31/2016 1:57:48 AM, Axonly wrote:

So 1+1 = 0.999 (R) + 0.999 (R)

If this is the case then:

So 1+1 = 1.888 (R) ?

Because this is the result of 0.999 (R) + 0.999 (R).

If they are the same then the result of this equation should be the same.
"Life calls the tune, we dance."
John Galsworthy
Mhykiel
Posts: 5,993
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1/31/2016 8:51:00 PM
Posted: 1 year ago
At 1/31/2016 8:36:42 PM, famousdebater wrote:
At 1/31/2016 1:57:48 AM, Axonly wrote:

So 1+1 = 0.999 (R) + 0.999 (R)

If this is the case then:

So 1+1 = 1.888 (R) ?

Because this is the result of 0.999 (R) + 0.999 (R).

If they are the same then the result of this equation should be the same.

Maybe you should type that into a calculator.

If you type in .9999999999999999999999999 add to .9999999999999999999999999

You will get 1.99999999999999999999999998

That 8 is only because I could not type in .9 repeating. Essentially that 8 would never be present in .9 repeating plus .9 repeating.

So .9... plus .9... equals 1.9... which is 1+ .9... which is equivalent to 1+1 which equals 2.

Again when we correct for 1.8 error the conjecture holds true .9 repeating equals 1.
famousdebater
Posts: 3,964
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1/31/2016 8:52:00 PM
Posted: 1 year ago
At 1/31/2016 8:51:00 PM, Mhykiel wrote:
At 1/31/2016 8:36:42 PM, famousdebater wrote:
At 1/31/2016 1:57:48 AM, Axonly wrote:

So 1+1 = 0.999 (R) + 0.999 (R)

If this is the case then:

So 1+1 = 1.888 (R) ?

Because this is the result of 0.999 (R) + 0.999 (R).

If they are the same then the result of this equation should be the same.

Maybe you should type that into a calculator.

If you type in .9999999999999999999999999 add to .9999999999999999999999999

You will get 1.99999999999999999999999998

That 8 is only because I could not type in .9 repeating. Essentially that 8 would never be present in .9 repeating plus .9 repeating.

So .9... plus .9... equals 1.9... which is 1+ .9... which is equivalent to 1+1 which equals 2.

Again when we correct for 1.8 error the conjecture holds true .9 repeating equals 1.

So irl if you were asked 1+1 you would answer 1.9999 (R)?
"Life calls the tune, we dance."
John Galsworthy
Mhykiel
Posts: 5,993
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1/31/2016 8:59:26 PM
Posted: 1 year ago
At 1/31/2016 8:52:00 PM, famousdebater wrote:
At 1/31/2016 8:51:00 PM, Mhykiel wrote:
At 1/31/2016 8:36:42 PM, famousdebater wrote:
At 1/31/2016 1:57:48 AM, Axonly wrote:

So 1+1 = 0.999 (R) + 0.999 (R)

If this is the case then:

So 1+1 = 1.888 (R) ?

Because this is the result of 0.999 (R) + 0.999 (R).

If they are the same then the result of this equation should be the same.

Maybe you should type that into a calculator.

If you type in .9999999999999999999999999 add to .9999999999999999999999999

You will get 1.99999999999999999999999998

That 8 is only because I could not type in .9 repeating. Essentially that 8 would never be present in .9 repeating plus .9 repeating.

So .9... plus .9... equals 1.9... which is 1+ .9... which is equivalent to 1+1 which equals 2.

Again when we correct for 1.8 error the conjecture holds true .9 repeating equals 1.

So irl if you were asked 1+1 you would answer 1.9999 (R)?

Please refer to my previous debate on this subject http://www.debate.org...

I would reply with 2. But I also would not state 2 is the only way to answer it.

Do you understand that 4 = 2^2= (2+2) = W30;16 = (1+3) = 4/1 = (4/2+4/2) = ect...

There are more then one way to answer and yet the answers be the same quantity.

what is 1/3 plus 2/3? If you keep them as fractions you have 3/3 which simplifies to 1.

But if you do the division which is the fraction sign you get .99 repeating.

Again 1 and .999 is equal. 2 different ways of saying the same thing.
dylancatlow
Posts: 13,069
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1/31/2016 11:02:56 PM
Posted: 1 year ago
At 1/31/2016 1:57:48 AM, Axonly wrote:
This blows my mind, here is the proof via algebra:
(R means repeating)

(1/9)=0.111(R)

9x(1/9)=0.111(R)

1=0.999(R)

Its so interesting how this works, normally I have limited interest in mathematics, but this takes the cake.


https://en.wikipedia.org...

The problem with this proof is that it takes for granted that which it attempts to justify. If .111 is actually equal to 1/9, rather than a mere approximation of it, then yes, .999 = 1. But that's kind of a lot to assume, since it's the exact question at issue. It's just the assumption restated in a different way, namely that you can assert the equivalence of two things by defining their difference to be so small as to be unspecifiable in precise mathematical terms.
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SeventhProfessor
Posts: 5,650
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1/31/2016 11:43:51 PM
Posted: 1 year ago
Yeah, that's not really a very good proof. The better one that tends to be more convincing is:

.999... = .999...
x10
10(.999...) = 9.999...
-.999...
9(.999...)=9
/9
.999...=1
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