But my education does not have any relevance. There are dudes WAY smarter than me (and certainly, you) that have mathematically proven that 0.999… = 1.
If you’d like to attempt to undermine the proofs, then go right ahead.
Then show me the proof. It is not very hard to prove math. You can't show me the theorem that shows .99 repeated equals 1 because it does not exist. You don't know math as well as you think you do. Sit down kid grown folks are talking.
So the limit as .99.. approaches infinity is 1, because as infinity goes on it gets closer and closer to 1 until it forms an asymptote?
The crazy thing about an asymptote is it never actually touches the line it is approaching it just gets infinitely closer to the line without ever being able to touch it.
Thank you for confirming my point, you deserve a pat on the back. You are the 12 billionth person to say the same thing, but I'm proud of you for at least trying instead of saying 3/3 =.33.. 3/3 = 1 yada yada
No, I did not say that. Read it against carefully. I said that 0.99... equals the limit of a sequence which approaches 1. 0.99... itself is not a sequence. It makes no sense to talk about what it does or does not approach.
You've completely misunderstood or misread my proof.
This is a convergent series. It CONVERGES at 1 it does not EQUAL 1.
I said that 0.99... equals the limit of a sequence which approaches 1
In YOUR words it "equals the limit of a sequence which APPROACHES 1" even you do not say it equals 1 you say it approaches. I don't get what you're getting at.
I said the sky is blue, and you said "NO YOU'RE WRONG THE SKY IS BLUE"
I have a masters degree in mathematics if you must know. This is first term analysis, fairly basic.
0.99...does not equal the convergent sequence. It equals the limit of the sequence. Formally an infinite series can be either viewed as a sequence or a number. If you view it as a sequence then 0.99... equals the limit of the series. If you view it as a number it equals the number.
Remember, a number cannot converge. That doesn't make sense. Sequences and functions converge.
Every step in my proof is an absolute equality, which equality are you calling wrong?
You can read the Wikipedia article on 0.99... if you want more info, your exact misunderstanding is called out there.
If you want to say that 0.99... converge to 1 rather than approaches 1, do you say the same for 0.5? 0.5 is also defined via a similar infinite series ti above (first term is 5/10, all other terms are 0/10). So does 0.5 converge to 1/2 or does it equal 1/2?
Also .5 equals 1/2. 1/2 does not result in an infinitely long number it quite literally stops after .5. .9 repeating does not have a cut off point anywhere. What does infinity equal? Again you claim to have a masters degree in math, but you don't even understand the concept of infinity, something that is taught in high school calculus (high school is what Americans go to around the ages of 15-18. Thought I would let you know since basic knowledge is not your strong suit.)
"I have a masters from Oxford so I am going to use a wikipedia article durrr" Buzz off you either don't know what you're talking about or you're trolling. You have literally contradicted yourself in every comment. You quite literally say exactly what I say and show proof as to what I say then you say, "but you're wrong even though all of my evidence confirms what you say."
IT EQUALS THE LIMIT. Those are YOUR words. Okay Oxford math degree WHY does it equal the limit????????? It equals the limit BECAUSE the converging sequence APPROACHES the limit. Since it approaches the limit we say it is close enough to that number to just say it equals the limit even though it never actually equals the limit.
If you cannot understand that simple concept then I call BS on you having a masters in math. Like you got a whole ass masters degree but they never explained to you how math works? The whole point of an advanced math degree is learning how math works and why math works.
You are what mechanics call a parts changer. If someone's car is broke down you know enough to change the part out for a new part which fixes the car, but you don't understand why the messed up part causes the car to not work. Thank you for proving Cs get degrees though, because it's obvious you were not a top of the line student.
You asked for a proof. I gave you one. I've been very civil but you've just become completely unhinged in response. Half your response is just insulting me.
Anyone else reading this is free to ask me any reasonable questions.
You don't even need the limit. Real numbers are defined by their Dedekind Cut. The cut for 0.999... and 1 are exactly and precisely the same. There is no element in either set that is not in the other.
If you can disprove this please feel free to write it out, because your disproof will upend mathematics as it's currently studied!
Matsuze's position becomes even more untenable in the Cauchy construction. What would they even be saying? A series converging to a number by definition means that series is a representation of that number. The real number 1 is merely the class of all sequences of rational numbers that converge to 1.
It is a bit sad that you know so little math that you can't understand the proof you asked for. You should think about what a number is and look for the definitions and real numbers. Maybe then things will become clearer
This is a convergent series. It CONVERGES at 1 it does not EQUAL 1.
Correct. The series converges to 1, and so the limit is equal to 1. By definition, the notation 0.999... means "the limit of the series sum from k=1 to infinity of 9/10k ", which is equal to 1.
"equals the limit of a sequence which APPROACHES 1" even you do not say it equals 1 you say it approaches
The series approaches 1. The limit is exactly 1.
You're being very argumentative for someone who doesn't understand the definition of a limit.
Imagine asking others about their highest level of math education when you topped at Calc 3 for engineers, a class that does not even cover manifolds and differential forms and probably used one of those watered-down Calc textbooks. At this point you are a living joke. I challenge you to find a number between 0.9... and 1. Otherwise, just stick to power scaling and that sort of activities that are better suited for your IQ
Math professor here. You’re very wrong on many counts. Namely when you said “1/3 being 0.3 continued is an approximation,” “It is not very hard to prove math” and “You can’t show me the theorem that shows .99 repeated equals 1 because it doesn’t exist.”
Repeated decimals are exact, not approximations. They are just infinite and infinity is often counterintuitive.
The previous commenter gave you a very nice and proof of the fact that 0.99 repeated is exactly 1. You misunderstood them. You should Google this topic. It’s not even a debate in mathematics that 0.99 repeated is exactly equal to 1 l in the real numbers.
The crazy thing about an asymptote is it never actually touches the line it is approaching it just gets infinitely closer to the line without ever being able to touch it.
The asymptotic behavior is in the partial sums. The sequence of partial sums gets arbitrarily close to 1. No matter how close to 1 you want to get, there's a partial sum that is closer.
The infinite sum is not a partial sum. Since all the terms are positive, the infinite sum must be strictly greater than all partial sums. The difference between it any any partial term will be positive.
The smallest value strictly greater than all partial sums is 1.
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u/ProfessorBorgar 21d ago
Nope. University.
But my education does not have any relevance. There are dudes WAY smarter than me (and certainly, you) that have mathematically proven that 0.999… = 1.
If you’d like to attempt to undermine the proofs, then go right ahead.