This is not a proof as you start with the answer, albeit disguised as a known truth. Here is a real proof. Start by assigning the recurring decimal a variable.
x = 0.9999...
Now calculate 10 times this by shifting the decimal place.
10x = 9.9999...
You can then subtract the second equation from the first. Note that all the digits after the decimal cancel out, leaving us with the following.
9x = 9
x = 1
Therefore, 0.9999… = 1. Infinity does weird things!
can 0.3• + 0.3• + 0.3• be really be added to equal 0.9• the same way that 0.3 + 0.3 + 0.3 = 0.9 though? and if so, is it proven or assumed? im not saying ur wrong btw, just asking. and does 0.000…001 equal 0?
0.3• has infinte decimals, 0.0000…001 does not. No matter how many zeroes you put before the one, there will never be infinite zeroes, so it’s not equal to 0.
You simply cannot have “Infinity + 1” decimals, since infinity + 1 = infinity.
I’m not a math person at all, so I’m not really debating your proof, but it seems to me that if 0.9• = 1, then what does 0.1• equal? It “fits” perfectly into the “space” between 0.9• and 1, but if 0.9•=1 then 0.1• should equal 0, right? Except it doesn’t, because 0.1<0.1• and 0.1 definitely isn’t 0.
I definitely understand why some religious people think numbers are a tool of Satan.
debatable
Not really.
1/3 = 0.3•
1/3 + 1/3 + 1/3 = 0.3• + 0.3• + 0.3•
3/3 = 0.9•
1 = 0.9•
And that’s only one proof, there are others.
This is not a proof as you start with the answer, albeit disguised as a known truth. Here is a real proof. Start by assigning the recurring decimal a variable.
Now calculate 10 times this by shifting the decimal place.
You can then subtract the second equation from the first. Note that all the digits after the decimal cancel out, leaving us with the following.
Therefore, 0.9999… = 1. Infinity does weird things!
can 0.3• + 0.3• + 0.3• be really be added to equal 0.9• the same way that 0.3 + 0.3 + 0.3 = 0.9 though? and if so, is it proven or assumed? im not saying ur wrong btw, just asking. and does 0.000…001 equal 0?
0.3• has infinte decimals, 0.0000…001 does not. No matter how many zeroes you put before the one, there will never be infinite zeroes, so it’s not equal to 0.
You simply cannot have “Infinity + 1” decimals, since infinity + 1 = infinity.
okay…i dont understand but ill trust you
There is actually a smallest number, typically denoted by a lower case epsilon, which is infintesimally small, typically used in calculus proofs.
I’m not a math person at all, so I’m not really debating your proof, but it seems to me that if 0.9• = 1, then what does 0.1• equal? It “fits” perfectly into the “space” between 0.9• and 1, but if 0.9•=1 then 0.1• should equal 0, right? Except it doesn’t, because 0.1<0.1• and 0.1 definitely isn’t 0.
I definitely understand why some religious people think numbers are a tool of Satan.
0.1111… is equal to 1/9. 0.0000… is trivially equal to 0.