What is wrong in this?

1 = (1 x 3)/3
1 = (0.333333333....33) x 3
1 = 0.99999..999
=> 0.0000....001 = 0
=> 1/10^ ∞ = 0
=> 1 = 0

Note by Ksg Sarma
3 years, 3 months ago

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First off, 0×0 \times \infty isn't defined. For more info, refer to indeterminate forms.

Secondly, the last equation should be limn110n=0 \lim_{n \to \infty} \frac{1}{10^n} = 0

Rather than 110=0 \frac{1}{10^{\infty}} = 0

Also, note that limn0×10n=0 \lim_{n \to \infty} 0 \times 10^n = 0

But, limn110n=0⇏limn0×10n=1\lim_{n \to \infty} \frac{1}{10^n} = 0 \not \Rightarrow \lim_{n \to \infty} 0 \times 10^n = 1

Deeparaj Bhat - 3 years, 3 months ago

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1/10^ ∞ is not exactly equal to 0 its value is too small and greater than 0 so when i multiply it with 0 it should be 0 . And according to your 1st statement 1 is undefined

ksg sarma - 3 years, 2 months ago

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110\dfrac{1}{10^{\infty}} isn't even a number!

Deeparaj Bhat - 3 years, 2 months ago

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moreover the main problem is with 3rd step where i am getting 1 is exactly equal to 0.999999..9999

ksg sarma - 3 years, 2 months ago

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There are so many errors that you've made in the above note.

First error

The .33333....333.33333....333 you wrote implies that the 33s will end since the last 3 isn't followed by ...... to imply that it repeats infinitely

Second error

This follows from your first and is very similar.Again.you're implying that the 99s will end sometime,which they don't because the 9s repeat infinitely.(occurs in line 3)

Third error

This doesn't even make sense.If something equals something,subtracting them from each other will result in exactly 00.This follows from your other errors too.(occurs in line 4)

Fourth error

You can't put .000..1.000..1 equal to 110\frac{1}{10^{\infty}} because you can't do arithmetic with infinity,it's a concept not a number.

Fifth error

Let's assume you used the correct way to express it which is limn110n=0\lim _{n \rightarrow \infty}{\frac{1}{10^{n}}}=0,you can't multiply each side by 10n10^n since it's in the limit,and it's not a constant.

Hamza A - 3 years, 2 months ago

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in the 1st error you said , tell me how many no. of 3's are there in the middle then I agree that it will end and all the errors are similar

ksg sarma - 3 years, 2 months ago

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@Ksg Sarma the 3s don't end,they repeat infinitely

Hamza A - 3 years, 2 months ago

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0.999=10.999\ldots = 1 exactly!

Deeparaj Bhat - 3 years, 2 months ago

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You can't play with infinity digit number like that!

Darmawan Putra Wijaya - 3 years, 3 months ago

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why don't u just make wiki

Darmawan Putra Wijaya - 3 years, 2 months ago

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