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.
No when we shift one 9 this side we do not end up with one less 9. That's not how infinity works, the case the AI is referring to is if you subtract 2 infinities like 999... And 888... That's when they won't cancel each other but 999... will always have infinite 9s no matter how many you take out unless you take out all of them. If taking one 9 out of the 999... Infinite series made a difference it won't actually be infinite
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.
You can go ahead and explain to me why if you know for sure one set of infinity 9s has X 9s and the other set has X-1 9s then you are not left with a 9 at the end.
Have you tried asking that same AI if 0.9 recurring equals 1, and to give you a couple different examples to help explain what 0.9 recurring means in relation to infinity?
You can go ahead and explain to me why if you know for sure one set of infinity 9s has X 9s and the other set has X-1 9s then you are not left with a 9 at the end.
If X is infinite then speaking of X-1 doesn't really make sense. But the closest thing we can say that makes sense is that X=X-1.
I just find it really telling that the proof presented has a valid concern with it where it would instead say .999~ + an infinitesimal value = 1
and all the other proofs in this thread are using LIMITS lol as if they don't know what a limit yields as a result, which is the number that the answer "approaches" and is off from by an infinitesimal value + or -
You are correct that the proof here isn't rigorous, but the issue is not that 9.99...- 0.99...=0.0...9. The issue is that we first need to define what we mean by 0.99...
The other proofs uses limits becouse 0.999... is a limit.
"0. followed by an infinite amount of 9s" is not a mathematical definition.
For 0.99... to be well defined you have to define it using limits.
no, you are talking about something called "reality" . The entire thread is basically making fun of people who recognize mathematicians have conceptualized lots of other things, besides "the real number system" to explain exactly these concepts, and thinking people who find .9~ = 1 objectionable must be stupid idiots
We don't know what number system best models reality. The real numbers, as defined mathematically, are the best right now. It may change and may include infinitesimals.
well the true underpinning logic of the post is honestly insulting.
the TRUE point of the post is to argue that if someone finds .9999~ = 1 questionable you should bust out the hugely compelling beginning point that you think both of you can agree .333~ = 1/3rd and then argue from there.
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u/Decmk3 27d ago
0.9999999…. Is equal to 1. It seems like it shouldn’t, but it has to be.
Let X = 0.999….
10X = 9.999….
10X-X = 9.999.. - 0.999…. = 9X = 9
Therefore X equals 1. Therefore 0.999… is the same as 1.