/sci/ - Science & Math » Thread #12679828

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Anonymous Mon 08 Feb 01:12:51 2021 No.12679828 View Reply Original Report

Quoted By: >>12679851 >>12679865 >>12679869 >>12679870 >>12679877 >>12679928 >>12680028 >>12680120 >>12680666 >>12680744 >>12680820 >>12680847 >>12680925

How can I prove to my friend that 0.999..... = 1. He keeps saying that 0.99... approaches 1 but never actually reaches it.

Anonymous

Anonymous Mon 08 Feb 2021 01:20:52 No.12679851 Report

Quoted By:

>>12679828
Perhaps explain to him what the word "approach" means. Because this isn't it.

Anonymous

Anonymous Mon 08 Feb 2021 01:23:17 No.12679856 Report

Quoted By: >>12679861

If 1/3 = .333
then 3/3 = .9426739294193919

Anonymous

Anonymous Mon 08 Feb 2021 01:24:45 No.12679861 Report

Quoted By: >>12679867

>>12679856
1 over 3 isnt .33 are you a baanket

Anonymous

Anonymous Mon 08 Feb 2021 01:27:03 No.12679865 Report

Quoted By: >>12679871

>>12679828
1/9 = 0.1111111...
1 = 9/9 = 9*(0.1111111...)
qed. done.

Anonymous

Anonymous Mon 08 Feb 2021 01:27:46 No.12679867 Report

Quoted By:

>>12679861
It's not .33 it's .333.

Anonymous

Anonymous Mon 08 Feb 2021 01:28:30 No.12679869 Report

Quoted By:

>>12679828
1/9 = 0.1111111...
1 = 9/9 = 9*(0.1111111...) = 0.999999....

so 1 = 0.999999....

done.

Anonymous

Anonymous Mon 08 Feb 2021 01:29:01 No.12679870 Report

Quoted By:

>>12679828
$\sum_{i=1}^\infty 1/10^i= 1/9$

Anonymous

Anonymous Mon 08 Feb 2021 01:29:09 No.12679871 Report

Quoted By:

>>12679865
0.11.... is not 1/9 it only approaches 1/9 but never reaches it.

Anonymous

Anonymous Mon 08 Feb 2021 01:32:55 No.12679877 Report

Quoted By:

>>12679828
If you can't explain it you don't understand it either lel.
And anyone saying its because 1/9 = 0.111... is just using circular logic.

Anonymous

Anonymous Mon 08 Feb 2021 01:34:44 No.12679883 Report

Quoted By: >>12679890 >>12680748

You're correct that they are equal. One trick would be

10(.999...)=9.99...
Now subtract .999... from both sides.
9(.999...)=9
Now divide by 9
.999...=1

Anonymous

Anonymous Mon 08 Feb 2021 01:37:22 No.12679890 Report

Quoted By:

>>12679883
>10(.999...)=9.99...
You forgot to add 0. The actual answer is 9.99...90.
Like for example 10*32=320. You shift the decimal point to the left and add 0.

Anonymous

Anonymous Mon 08 Feb 2021 01:38:36 No.12679895 Report

Quoted By:

10(0.99999...)=9.999999...
9.999999...-0.99999...=9
(10-1)(0.99999...)=9
9(0.99999...)=9
0.99999...=9/9=1
So 0.99999...=1

Anonymous

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Anonymous Mon 08 Feb 2021 01:49:05 No.12679928 Report

Quoted By:

>>12679828
$\displaystyle\rlap { \lower{-1.5em}{You ~can't~ travel }} \rlap { \lower{-1.9em}{Cant}} \rlap { \lower{-2.5em}{ ~~~~~~~~can't ~travel~ the~ speed}} \rlap { \lower{0.6em}{of~ light}} \rlap { \lower{0.5em}{of ~~light}} \rlap { \lower{1.9em}{only~ a~ fraction}} \rlap { \lower{2.5em}{ ~~~~~fraction }} \rlap { \lower{2.7em}{ ~~~~~~fraction }} \rlap { \lower{3.4em}{ ~~~~~~~~~~~~~~~~~ 0.999^{9^{9^{9^{9^{9^{9 ^{9^{9^{9^{9^{9^{9^{9}} }}}}}}}}}}}}} \rlap { \lower{3.5em}{ ~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~=1}} \rlap { \lower{3.4em}{ ~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~=1}} \rlap { \lower{4.2em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.25em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.1em}{you~ can ~travel ~at ~the ~speed ~of ~light}} \rlap { \lower{4.7em}{you~ can ~travel ~at ~the ~speed ~of ~light}}$

Anonymous

Anonymous Mon 08 Feb 2021 01:53:44 No.12679946 Report

Quoted By: >>12679951 >>12679971

$\int_{0}^{\int_{0}^{\infty} 1-10^{-x} dx} x dx$

Anonymous

Anonymous Mon 08 Feb 2021 01:54:46 No.12679951 Report

Quoted By:

>>12679946
What the fuck is that

Anonymous

Anonymous Mon 08 Feb 2021 02:01:06 No.12679971 Report

Quoted By:

>>12679946

How do I prove that:
$\int_0^1 dx =1$
by $\varepsilon$ and $\delta$ ,
and Riemann $\sum_\infty$ sums?

Anonymous

Anonymous Mon 08 Feb 2021 02:17:05 No.12680028 Report

Quoted By:

>>12679828
If you're talking abstract numbers than your friend is right. If you're talking about actual physical measurements than there is going to be uncertainty, which depending on the accuracy of the measurement, could definitely be interpreted as having a value of one, if it falls within the uncertainty bounds. Make the argument that math without physics is just a logically consistent set of rules and not good for anything. Application of math is everything, and that means use in the physical world with physical measurements, that would include uncertainty in said measurements. Go full utilitarian on him.

Anonymous

Anonymous Mon 08 Feb 2021 02:46:06 No.12680120 Report

Quoted By:

>>12679828
an infinite process does not terminate, therefore it cannot be equal to anything. it is merely a process that gets closer to 1 the longer you do it, but it has no value as a singlular number because you can't have infinite digits.

Anonymous

Anonymous Mon 08 Feb 2021 06:26:15 No.12680666 Report

Quoted By: >>12680737

>>12679828
$\lim_{x \to \infty} \frac{10^x - 1}{10^x} = 1$
That's where "approaching" is relevant. The actual number 0.999... is just equal to 1.

Anonymous

Anonymous Mon 08 Feb 2021 06:58:11 No.12680733 Report

Quoted By:

You can't, it's a theological question, like angels dancing on the pinhead.

Anonymous

Anonymous Mon 08 Feb 2021 07:00:27 No.12680737 Report

Quoted By:

>>12680666
0.999
post 666

but what does it mean.

Anonymous

Anonymous Mon 08 Feb 2021 07:02:30 No.12680744 Report

Quoted By: >>12680756

>>12679828
If 0.999 is actually 1
then 0.998 is the same as 0.999
Therefore 0.998 = 1 as well

When does the madness end.

Anonymous

Anonymous Mon 08 Feb 2021 07:04:30 No.12680748 Report

Quoted By:

>>12679883
That's such a brilliant proof! Let me prove Fermat's theorem this way.
2*a^n+2*b^n=2*c^n does not have any solutions for natural a,b,c and natural n>2.
Therefore a^n+b^n=c^n does not have any solutions for natural a,b,c and natural n>2.
Q.E.D.

Anonymous

Anonymous Mon 08 Feb 2021 07:07:23 No.12680756 Report

Quoted By:

>>12680744
I think it will end somewhere on 0.686

Anonymous

Anonymous Mon 08 Feb 2021 07:10:20 No.12680768 Report

Quoted By:

In practice they are equal, but that's also true for 0.9999 and 1.0001
In theory it fully depends on your definitions.

Anonymous

Anonymous Mon 08 Feb 2021 07:29:55 No.12680820 Report

Quoted By:

>>12679828
You can't just cancel out the 2's algebraically. If this is a limit, then as x approaches infinity then 2 would grow to be insignificant, and the equation would approach 1 which would be represented by an equals sign for limits.

Anonymous

Anonymous Mon 08 Feb 2021 07:48:01 No.12680847 Report

Quoted By:

>>12679828
Give him 0.999... apples and directly demonstrate that is the same as having given 1 apples.

Anonymous

Anonymous Mon 08 Feb 2021 07:49:14 No.12680849 Report

Quoted By:

With the geometric series 9* (1/10)^k, k from 1 to infinity.

Anonymous

Anonymous Mon 08 Feb 2021 08:07:13 No.12680880 Report

Quoted By: >>12680889

If infinity is nonsense, then ... symbol is nonsense too.
If infinity is meaningful, then there is no problem with infinitely small difference between numbers.

Anonymous

Anonymous Mon 08 Feb 2021 08:11:31 No.12680889 Report

Quoted By: >>12680894

>>12680880
>then there is no problem with infinitely small difference between numbers
you're right, there's no problem with 0

Anonymous

Anonymous Mon 08 Feb 2021 08:14:12 No.12680894 Report

Quoted By:

>>12680889
Great, then 0.999... isn't equal to 1 with the difference of 0.

Anonymous

Anonymous Mon 08 Feb 2021 08:34:18 No.12680925 Report

Quoted By: >>12680930

>>12679828
Just ask him what number is between 0.999... and 1, if he says it's 0.000...1 then he's wrong and since there isn't a number between them it's the same number. QED

Anonymous

Anonymous Mon 08 Feb 2021 08:37:35 No.12680930 Report

Quoted By:

>>12680925
>f he says it's 0.000...1
What if he says it's a non zero infinitesimal value?

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