This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .

Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.

Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold

- bulleted - list

bulleted

list

1. numbered 2. list

numbered

list

Note: you must add a full line of space before and after lists for them to show up correctly

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

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

First error

The $.33333....333$ you wrote implies that the $3$s 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 $9$s 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 $0$.This follows from your other errors too.(occurs in line 4)

Fourth error

You can't put $.000..1$ equal to $\frac{1}{10^{\infty}}$ 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 $\lim _{n \rightarrow \infty}{\frac{1}{10^{n}}}=0$,you can't multiply each side by $10^n$ since it's in the limit,and it's not a constant.

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in`\(`

...`\)`

or`\[`

...`\]`

to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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

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

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

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

But, $\lim_{n \to \infty} \frac{1}{10^n} = 0 \not \Rightarrow \lim_{n \to \infty} 0 \times 10^n = 1$

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

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

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

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

Third errorThis doesn't even make sense.If something equals something,subtracting them from each other will result in exactly $0$.This follows from your other errors too.(occurs in line 4)

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

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

Log in to reply

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

Log in to reply

Log in to reply

$0.999\ldots = 1$ exactly!

Log in to reply

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

Log in to reply

why don't u just make wiki

Log in to reply