Mistake in the proof?
1/3 = 0.333333....
1/3*3 = 0/33333*3
1=0.9999999999.........
no approximation
they r equal exactly
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Well, its not that wrong, but not quite right either.
You see, 1/3 is 0.333333.... till infinity.
Infinity by any standards is a very large number.
So, when multiplied by 3, the number becomes 0.9999999..... till infinity.
This value is so close to one, that it can be approximated to 1.
Like saying that 0.9 is close to 1, but 0.99 is closer, 0.999 is even closer and so on.
Even better would be to say that technically, a plane mirror has no radius of curvature as it is not curved, but mathematically, its radius is infinity.
Since the value goes on to infinity, it lands very close to one and although technically isn't exactly 1, but is considered to be 1.
You see, 1/3 is 0.333333.... till infinity.
Infinity by any standards is a very large number.
So, when multiplied by 3, the number becomes 0.9999999..... till infinity.
This value is so close to one, that it can be approximated to 1.
Like saying that 0.9 is close to 1, but 0.99 is closer, 0.999 is even closer and so on.
Even better would be to say that technically, a plane mirror has no radius of curvature as it is not curved, but mathematically, its radius is infinity.
Since the value goes on to infinity, it lands very close to one and although technically isn't exactly 1, but is considered to be 1.
UnknownDude:
Thanks ^_^
this means that 0.999999...... = 1 u r agreeing ? then we can prove that 0.9999998.......... =0.99999.......... Hence 0.999998..... = 0.99999 ....... This way after solving this pattern infinite times we will get 0=1 ....... [there should be a genuine mistake in the proof .......i am sure]
Like I said, technically not 1, but considered 1
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