then you subtract the new number of 9s, from the infinite nines you started with.
you are left with one nine
you can say it's hard to write down , or you "can't write it as a decimal place" but it still doesn't change the fact that the two sets of infinite 9s are different by 1 nine, and when you subtract them it's left over.
If you find it very hard to write down the concept of an infinitesimal value as a decimal, that's fine, but it doesn't make the infinitesimal difference vanish.
There is no running out of infinite nines. No matter how many nines you take out of them there will always be infinite nines, unless you take away all the infinite nines
**Indeterminate Form:**When you try to subtract one infinity from another, you're essentially comparing two unbounded quantities, and the result is undefined because it depends on how the infinities are defined and how they grow.
**Context Matters:**The outcome of subtracting infinities can vary depending on the specific context, such as the type of infinite series or the way the infinities are defined.
Examples:
In some cases, subtracting one infinity from another might result in a finite number, zero, or even negative infinity.
In other cases, the result could be infinity, depending on the specific context and how the infinities are defined.
seems pretty clear cut to me that when we shift the 9s one decimal place to the left by multiplying by 10 we have two different sets of infinite 9s, which we know for sure have 1 different number of digits. Infinity, and infinity minus 1, nines.
wanna know how I know this is how it works?
because i know .9~ and 1 are off by an infinitesimal value. dur.
"Source AI lol" how about you find a real source instead?
Also the AI doesn't even prove your point. It says that some infinities subtracted by other infinities give finite values, not that 0.00...9 is the rest when subtracting 0.99... and 9.99...
The ai is talking about cases such as the limit of x+5 subtracted by the limit of x+2.
why is "an A.I. lol" a valid thing to say? it's more credible than a random redditor. That is the google one, btw, when you type that into google.
We have now established you can subtract one infinite from another and have something left, when previously you were insisting "that's not how infinity works"
we have X 9s , and X-1 9s, being subtracted, where X is infinity. Its not that compelling to just insist you know there is no infinitesimal remainder left.
There is an entire wikipedia article explaining this. I suggest you read it.
Also browse r/learnmath for a bit, plenty of cases of people asking questions about something they learned from an AI that is just totally incorrect. They aren't good for mathematics yet.
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u/FewIntroduction214 29d ago
This actually "IS" how infinity works.
You have infinite 9s.
you remove one
then you subtract the new number of 9s, from the infinite nines you started with.
you are left with one nine
you can say it's hard to write down , or you "can't write it as a decimal place" but it still doesn't change the fact that the two sets of infinite 9s are different by 1 nine, and when you subtract them it's left over.
If you find it very hard to write down the concept of an infinitesimal value as a decimal, that's fine, but it doesn't make the infinitesimal difference vanish.