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File: Infitesimal limits.png (16 KB, 496x286)
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If we can have [math]\aleph_{0}[/math], why can't we accept that the infinitesimal isn't 0?
>>
>>12746851
>Step 6
That's not how base conversions work
>>
>>12746912
Oh really? Tell me, what's [math]4/10_{5}[/math] in base 10?
>>
>>12746923
0.999...
>>
>>12746851
>>12746912
You have committed a grave mistake.
[math]
0.4..._5 \neq 0.8..._{10}
\\
Rather:\\
\Sigma_{n\to\infty} 4(5^{-n})
\\Think\ about\ it.
\\(0.44)_5 = (4 * 5 ^{-1} + 4 * 5 ^{-2})_{10} = (0.832)_{10} \neq 0.8..._{10}
[/math]
I was just writing that.
>>
>>12746930
You're seriously telling me this many things: IIII divided by this many: IIIII is not 4/5 in base 10, but actually 0.999...?
>>
>>12746940
No, I thought you were talking about 0.444..., since that's in step 6 that I mentioned. Why did you change the subject?
>>
>>12746930
Nope,
Σn∞4/(5^-n) - Σn∞9(10^−n)
=
Σn∞[2^-n x 4 - 9]/(10^(−n))

Since 2^-n x 4 - 9 < 0 if n > 0, the result is negative.
So 4/105 in base 10 is smaller than 0.9999...
Mathematicians sure lack rigor these days!
>>
>>12746851
because that's how the real numbers are defined, and they're defined this way because it reflects what we want and expect of them. we want the derivative to be EXACTLY the slope, we want the integral to be EXACTLY the area, not something "infinitesimally" close to it. the archimedean property and standard definition of limit gives you precisely this. feel free to invent your own algebraic structure though, it's not like anyone's stopping you.
>>
File: zolzm.png (10 KB, 310x159)
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>>12746934
>>12746963
base 5 screwing with my head. I should have converted to fractions.
0.44 is 24/25, which is not 0.832.
>>
>>12746923
0.8
>>
>>12746851
step 6 is wrong, lol
>>
>>12746851
your whole thing is just a mess. play around with https://www.rapidtables.com/convert/number/base-converter.html for two minutes to find out that everything you wrote is garbage
>4/10 in Z5 is not .444... in Z5
>.444... in Z5 is not .888... in Z10
also, 4/10 in Z5 is more analogous to 9/10 in Z10 than to 9/9. you should have used 4/4 in Z5 and discovered that you're a moron and dividing a non-zero number by itself is always 1



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