Thread: Does 0.9 repeated = 1?

An exception of what?

Not existing outside of comprehension.

No, but it can exist outside my comprehension.

The whole metaphysical, everything is just a perception of a perception yadda yadda yadda doesn't apply in theoretical mathematics. Or at least it shouldn't. If a question about the principles of math can be turned into some new-age discussion then nothing is safe from that argument...

The thing about maths is that it isn't actually true in itself. Godel showed that you can't use a consistent system to prove the validity of the system.

To give an example... geometry. I suppose you consider geometrical proofs to be absolutely true (eg c2 = a2 + b2 -2absinC). However they are actually a science; straight lines and such are not actually real. In fact Euclidian (traditional) geometry is only an approximation of reality. There are other types of geometry which are completely logical, such as hyperbolic geometry, but do not approximate so well to our reality; in fact the geometry of our universe is warped in a four dimensional construct called spacetime which is neither Euclidian nor hyperbolic.

The point is that we tend to build up axioms from reality; however they are imperfect models. This is why I say, for example, geometry, is not 'real'. You can extend this idea to numbers.

Numbers don't lie.

One plus one is two.
It is equally true that four times seven is twenty eight.
It is equally true that .99 repeating is 1.

There are other types of geometry which are completely logical, such as hyperbolic geometry, but do not approximate so well to our reality; in fact the geometry of our universe is warped in a four dimensional construct called spacetime which is neither Euclidian nor hyperbolic.

The accuracy of hyperbolic geometry depends on what the shape of the universe is, which is presently unknown.

However they are actually a science; straight lines and such are not actually real.

Maths isn't science. Plus, saying straight lines and such are not actually real is obvious, its a abstract language.

The thing about maths is that it isn't actually true in itself. Godel showed that you can't use a consistent system to prove the validity of the system.

No, he didn't. He proved that if you have a consistent system it is incomplete vice versa, he said nothing about validity of the system.

Originally Posted by drewmandan

I'm saying the crude method of subtraction you're using doesn't work in general. It's a shortcut taught to school children, not to be taken as something rigorous.

What is taught to school children about subtraction is not bull shit. 9 - 5 really is 4. Do you say it is not?

Originally Posted by drewmandan

This quote is out of context, but I think you know what I'm referring to with the following.

The reals are defined on a structure of limits. The details are quite complicated, but in the reals, limits are how equality is defined, in this case. The reals are dense, so you can't use something as crude as whole number equality.

The reals are completely exact. 8, for example, is an exact number. It may be a figure involved in a situation of limits, but 8 itself is not a matter of limits. It is a 100% exact, specific figure.

Maths isn't science. Plus, saying straight lines and such are not actually real is obvious, its a abstract language.

Euclidian geometry can be classed as a scientific theory. If our space was actually severely warped, we would not have developed Euclidian geometry.

No, he didn't. He proved that if you have a consistent system it is incomplete vice versa, he said nothing about validity of the system.

Well, the implication is that truth exists outside of mathematics. There are things which are true, but not 'because' of mathematics, as they cannot be proved.

Numbers don't lie.

One plus one is two.
It is equally true that four times seven is twenty eight.
It is equally true that .99 repeating is 1.

That's a model of our experienced reality, in which when you get a collection of x things and jumble them up with another collection of y things then the amount of things you'll have is x + y. This is an axiom, but you can't prove it. In fact, it may well not be true on the non-classical scale.

Originally Posted by Xei

That's a model of our experienced reality, in which when you get a collection of x things and jumble them up with another collection of y things then the amount of things you'll have is x + y. This is an axiom, but you can't prove it. In fact, it may well not be true on the non-classical scale.

So 2 + 2 is somehow nonstatic, plural, or subjective or something? I know that such beliefs are a modern trend, even with certain high profile mathematicians and theoretical physicists, but I am far from convinced of it. I really want to see somebody demonstrate how 2 + 2 can be anything other than 4, in any case at all, ever. I started a thread in R/S that partly involved that issue, and it became one of the most chaotic threads I have ever seen on DV, outside of Senseless Banter.

I think too many modern mathematicians and theoretical physicists are putting way too much importance on humans and thinking the laws of the universe compose some kind of Salvador Dali painting where up is down and 3 = 7. The bull shit seems to be getting really thick.

2 + 2 = 4 is true as it is axiomatically defined. 2 + 2 = 2 would form another coherent system though, even though it would not represent much and would be completely useless. It is probably impossible to think of a situation in which it would be necessary because in the reality we experience 2 + 2 is always 4, just like it is probably impossible to comprehend multiple time dimensions and such things.

What I'm saying is that '2' doesn't exist. It describes an observed property of something (in set theory 2 is the set of all things with 'twoness' about them, such as two trees, two men, two sets, whatever). The symbol can then be manipulated according to rules based on observation to give true statements.

This is why people so frequently struggle with imaginary numbers. They don't realise that they are just a mathematical conception used to derive truths, just like all numbers.

++ 2 plus signs
++ 2 plus signs
4 plus signs in all

Right?

Uhuh.

Although a plus sign is a concept.

Originally Posted by Universal Mind

What is taught to school children about subtraction is not bull shit. 9 - 5 really is 4. Do you say it is not?

I said it's a special case. But try using that method to get the exact answer to pi-sqrt(2). Without using limits, you can't. You'll just be subtracting forever.

Originally Posted by Universal Mind

The reals are completely exact. 8, for example, is an exact number. It may be a figure involved in a situation of limits, but 8 itself is not a matter of limits. It is a 100% exact, specific figure.

8 is a natural number. But what about e? e is a real number that is defined (for example) as lim(n-->inf) {(1+1/n)^n}.

Originally Posted by drewmandan

I said it's a special case. But try using that method to get the exact answer to pi-sqrt(2). Without using limits, you can't. You'll just be subtracting forever.

8 is a natural number. But what about e? e is a real number that is defined (for example) as lim(n-->inf) {(1+1/n)^n}.

I agree that limits are a reality. I just think exact numbers are also a reality. Even figures that involve limits are exact. We just cannot express them with all digits included. But we can express other numbers with all digits included.

Originally Posted by Universal Mind

I agree that limits are a reality. I just think exact numbers are also a reality. Even figures that involve limits are exact. We just cannot express them with all digits included. But we can express other numbers with all digits included.

Ok, so what's your point? You were originally arguing that 1-0.9~ =/= 0. Do you now retract that?

Originally Posted by drewmandan

Ok, so what's your point? You were originally arguing that 1-0.9~ =/= 0. Do you now retract that?

No. Exact numbers exist, and I stand by that. I don't think that fact about exact numbers in general is part of any contradiction or paradox.

I also think infinite smallness exists. I am just still not sure how it is possible, though it apparently is. That is where there seems to be a paradox, and it has the same paradoxical nature as Zeno's Paradox. If I could ever resolve Zeno's Paradox, I think I could have a better grip on the nature of infinite smallness. Is infinite smallness an exact number? Probably not. Infinity is not a number, so I guess infinite smalleness is not a number either. Hmmmm..... Maybe that's the problem. The difference between 1 and 0.999... exists, but that difference is not a number?

When I am a senile 88 year old babbling off the wall stuff all the time, I think a lot of the babble is going to be about this stuff because I know it will probably deeply puzzle me for the rest of my life.

Infinite smallness

lim(x --> 0) x = 0

or even


lim(x --> infinity) 1/x = 0

Originally Posted by Kushna Mufeed

Infinite smallness

lim(x --> 0) x = 0

or even


lim(x --> infinity) 1/x = 0

That is probably about the best answer we can have regarding the difference between 1 and 0.999..., but I do not agree with the = part. Approaching 0 forever is not the same as equalling 0. So, the difference between those two numbers exists, but the difference is not a number. The two numbers are equal numerically, but do not have exactly the same value in another sense. The difference is not 0, but it is so much like 0 that it is almost okay to call it 0. So, uh, ... .

http://www.youtube.com/watch?v=c6wwmc9BvYg

Originally Posted by Universal Mind

I also think infinite smallness exists. I am just still not sure how it is possible, though it apparently is. That is where there seems to be a paradox, and it has the same paradoxical nature as Zeno's Paradox. If I could ever resolve Zeno's Paradox, I think I could have a better grip on the nature of infinite smallness.

Zeno's paradox really vexes you, huh? Might want to educate yourself in some calculus, champ.

lawl

Originally Posted by Universal Mind

That is probably the best answer we can have regarding the difference between 1 and 0.999... So, the difference between those two numbers exists, but the difference is not a number.

Actually, the difference is a number, as per the axiom that the real line is Cauchy complete. But of course, with your 6th grade math education you wouldn't know that.

Originally Posted by drewmandan

Zeno's paradox really vexes you, huh? Might want to educate yourself in some calculus, champ.
lawl

Nice answer! Why retake calculus when I can just read your empty comments of assholishness that do not clear up anything?

Originally Posted by drewmandan

Actually, the difference is a number, as per the axiom that the real line is Cauchy complete. But of course, with your 6th grade math education you wouldn't know that.

Do you realize that you are clearing up nothing, shit-head? I used to be a math teacher, and I wrote an algebra textbook. You are throwing around obscure terms with the hope that nobody will know what you are saying, but I do, and you are saying nothing that clears up the issue.

Infinity is not a number, so infinite smallness is not a number. If you disagree, give an actual counterargument. Do you know what a counterargument is?

Why be an asshole when it is not necessary? Explain that to us. Are you just a typical unoriginal troll, or do you just have the maturity of a neglected 6th grader? How old are you? Get a life. Dick.

Now explain how infinite smallness is a number. Don't just throw out a term and hide. Actually say something, for once. Then see a shrink about working on your obvious personality disturbance.

Originally Posted by Universal Mind

Do you realize that you are clearing up nothing, shit-head? I used to be a math teacher, and I wrote an algebra textbook.

Ok, so that's clearly bullshit. Unless the "algebra" you're referring to is "solving for x" and the textbook is meant for elementary school.

Anyway, since the metric space of the reals under distance as defined by absolute value of the difference is complete, all defined limits on the reals converge to a number. In this case, 0.

OK, now that this thread is reverting back to the immature insult throwing contest that is was before, I'll request for the THIRD time that it's locked again.