That ... MEANS the thing on the left IS the limit. 0.999... IS the limit of the sequence {0.9,0.99,0.999,...} — fdrake

I don't think so. .999... describes the series. The limit of it is infinitely far away.

Another argument, more or less following similar thinking, is whether a number could be found between 0.999... and 1.000... (like the mean).
If no such number can be found, then we might reasonably say they're one and the same. — jorndoe

But the problem is what does .999... mean? How many 9s are we talking about? An infinity of them, of course. But what is an infinity 'of' something?

Actually it does, that's why they use the equals sign. It's the entire essence of calculus. — Pantagruel

True. But they don't mean .999... = 1. They mean the Limit of the infinite sum = 1. There's a difference.
The sum being 9/10 + 9/100 + 9/1000 + ...

because that’s just what decimal notation means. And since the limit of the series of partial sums of that infinite series is 1, that means the total sum of that infinite series represented by 0.999... is also 1, so 0.999... = 1. — Pfhorrest

But it has to do with the way language is being used. 'The total sum' is not the same thing as 'equals'.

The total sum cannot be explicitly demonstrated. It is really a concept that cannot be substituted with 'equals'.

the ... means the limit is taken. IE, .999... = 1 — fdrake

Yes but 'limit' is not the same as 'equals'.

It comes down to how the language is used .9999... equals 1. This is not true. In calculus one is only allowed to say that a series converges to a limit. In this case the series is .999... and the limit is 1. That is, incorrectly speaking, .999...becomes one after an infinity of 9s. But you can't have 'an infinity of' 9s because infinity is not a number. So no, .999... is not 1. It only converges to 1. That is all the link you posted is showing. They are replacing 'tends towards the limit 1' with 'equals'.
You can say The limit = 1 but not .999...= 1

Thought is being and being is thought. In our modern ossified world we tend to believe thinking is just abstract machinations and 'logic' and such things. It is much broader than that.

Science has shown remarkable capability of verification, prediction and use.
How is is this possible if it is only the appearance of external reality (phenomena), not the external reality itself (noumena)? — Arthur Rupel

Look at it this way. If we surmise that what we perceive is analogous to what is really out there we may be able to make progress. For example, if we see something moving in a circular manner we can surmise that there is something out there that is changing in a cyclical manner - not necessarily a circular manner. So our experience is telling us something real.

Also, if we perceive something, assuming the analogy as above, we can then focus on a smaller detail of the perceived object. Then on a smaller detail and so on. We can then determine how these details are related to each other and assume that these perceived relationships between parts are also analogous to the actual relationships between the parts of the perceived object.

This process of endless division into smaller parts should be coherent and analogous to the coherence between the parts of the object itself. If there is coherence in our phenomenological perception, down to the finest detail, this coherence can be understood to reflect the actual coherence of the object itself because the object is the source of our perception.

In other words, if our perception is, in any way, analogous to what is really there, it should be analogous down to smaller and smaller details. We can then make a detailed map of what is really there.

The only other possibility is that nothing in our perception is analogous to what is actually there, which is philosophy gone mad.

So it doesn't mean anything? — tim wood

Isn't child abuse perverse? I don't see why one's subjective point of view needs to be meaningless. The sadist is acting out evil. The masochist wants freedom from self - without giving up self.

What is? — tim wood

That depends on one's subjective point of view.

if I adduce enough arguments to show that time is unreal, time might stop. In other words, there is a recognition that since one can speak however one pleases, that one can in some sense 'make true' whatever one pleases, just by talking about it. — Snakes Alive

Isn't this exactly what Lazerowitz is doing? Talking himself into his own truth? Maybe all philosophers do that, lol.

Sexuality is spirituality in bodily terms. Sexual distortion is spiritual distortion. Think about it...

What I've referred to as the (mono)theistic 'command to love' seems akin to masochistic rape-fantasy or self-abnegation: — 180 Proof

Masochism is a distortion of spirituality, not the other way round.

You have a point there I suppose. What means you by wise obedience? — TheMadFool

It means thinking about why religion tells us how to live. This is what Buddhism means by 'wise living'. But, of course, sometimes religion is corrupt.

To entertain the idea of false/misguided obedience is to sow the seeds of disobedience that ultimately leads to the rejection of god. — TheMadFool

The hope is that it would lead to wise obedience. Slavish obedience is not a good thing. Obedience should be understood rather than rejected at face value. There is a worthy goal in wise obedience.

one of the most effective methods to make normal people do immoral things is to convince him/her that s/he is doing god's will. — TheMadFool

That would be false or misguided obedience.

Are you defining discipline as obedience to one's self? — Pantagruel

Yes, but obedience to someone else can also be a good thing if that obedience has a purpose. An athlete needs to listen to and obey the trainer. Musicians need to be attentive to the conductor. Pupils needs to be obedient to the teacher. But obedience should be understood and its purpose needs to be understood. In evil obedience is slavery to a tyrant. But there are times when obedience is wise and good.

Isn't this slavery? A slave must obey his master's command and the master makes it clear that he has zero tolerance for any disobedience. — TheMadFool

It depends on what you mean by obedience. Obedience is essential for development. eg someone practicing music or art must have great discipline/obedience. A great tennis player must make their body obedient to their mind.
Wise obedience is a good thing if it leads to freedom. A good soldier must learn obedience. A bad soldier will get killed. One must try to understand why obedience is necessary and how it leads to freedom. Sloth and disobedience don't achieve anything worth while.

The vast majority of reality at every scale is space, that which we typically call nothing, or non-being. — Nuke

In our simple human definition of being, yes. God is energy and being. Space is God. There is nowhere where God is not (space is no-thing but not nothingness (there's a difference) It has positive being.)

Every act of creation is an act of destruction, and every act of destruction is an act of creation. — Nuke

Ultimately everything is evolving and moving forward. But you cannot judge these things in human terms. Even good and evil become unclear in the hurly-burly of human affairs. Ultimately being and life emerge from matter, time and space. We'll have to wait till the end to see how it all works out.

That was very poetic. I like your personal take on it. — Benj96

Glad you enjoyed it.

Wouldn't good have to be in reference to something? You know, good for who or what? — Nuke

The existence of the good as evidence for God's existence is hard to argue with. But yes, what is the good? Ultimately the good promotes life and being. Evil is ultimately non being. The good is unity. Evil is egoism and separation; the black hole detaches itself from everything else and becomes darkness.

Then how did energy ever give rise to mass (e=mc2)? If it cannot do anything to itself in a state of pure timelessness then how did it just spontaneously slow down and get "heavy" with matter in the first place. — Benj96

That's Higgs theory; mass is a slowing down of energy. Mass and matter are not substances, they are processes.

$\exists$ x = $\frac{1}{a_1^\frac{p - 1}{2}(mod p)}$
such that x = $\pm 1$

${\sqrt {ab \pm c} \over \sqrt{x/y}} \pm 1$

$a \equiv b (mod m)$

$\phi =$$\frac {1}{1 + \frac{1}{1 + \frac{1}{1 + ...}}}$

$\sum_{i=1}^{\infty}$

${\sqrt {2 - 1/\sqrt {2}}}$

2. The magnitude of the effect is proportional to the magnitude of the *effect* — TheMadFool

Shouldn't that be 'cause'?
Corruption moves away from the good which is love, life and being. Corruption moves towards hatred, death and non being. This is despair, hell. Call this karma if you will...

You sound like the opposite to a misanthrope; you believe in humanity and the fact that you see how people's behaviour is wrong shows you believe in standards of behaviour. As for being irritated - there will always be such people. Personally I choose to ignore them as far as possible. Gravitate towards better folk.

Thus, consciousness is needed to make physical reality meaningful.

Well, that goes without saying. How can meaning exist outside a mind? I think he is talking about something slightly different here.

'What did you do to the cat, Erwin? — Wayfarer

Schrodinger's Cat was not originally meant to be taken seriously. It was an illustration of the problems with emerging quantum mechanics at the time.

A lot of this confusion about things not happening until we 'observe' them has to do with a conflation between detection and observation, as if they were the same thing. But they are not.

Observation is when a scientist looks at the results of an experiment. That has nothing to do with how the experiments takes place or what the results are.

Detection is when a particle in the quantum universe/spacetime collides with an object (experimental apparatus) in physical spacetime. This is what determines the result of the experiment. Observation has nothing to do with it. After all, a scientist could wait months before observing the results of an experiment. Does that mean there are no results until he observes those results? I don't think so.

A lot of pseudo books have been sold on this 'changing reality by observing it' notion...

Patterns in mathematics are often simplifications. Also, some patterns apply in infinitely many situations. For example, if p is prime, a^p leaves a remainder a when divided by p: 3⁵ = 243 which leaves remainder 3 when divided by five.

This applies to all primes so we can say 733⁶¹⁰⁶⁹⁹ leaves remainder 733 when divided by 610699. We can know this without doing the calculation. Simplicity and universality of patterns in mathematics are what the mathematician seeks.

The category is bolded. See left. — Outlander

Ah. Thank you.

At least in the android store. — Benkei

Thanks.

check out the app xsection — Benkei

Where is that?

It is possible for both to suspend empathy. In fact, the psychopath is not devoid of empathy (that's almost an urban myth). The psychopath has repressed empathy and conscience with such ferocity he does not feel it. He supresses it because if he didn't he could not indulge in his monstrous behaviours.

If you commit a crime against a psychopath s/he will tell you in no uncertain terms what you did was wrong and why it was wrong and how you should be punished. But s/he forgets all this when it is the other way around.

imagine six crosses arranged in two rows of three crosses each, one row directly above the other. I can equally imagine the same six crosses as three columns of two each. Therefore 2 × 3 = 3 × 2. I not only notice that 2 × 3 is in fact equal to 3 × 2, I understand why 2 × 3 must equal 3 × 2. — The mathematical world - James Franklin

This is an example of induction (observation) awakening our powers of deduction. Resulting in deducing the commutative nature of multiplication: 2 x 3 = 3 x 2.

This visual proof is a bit more elegant: — InPitzotl

Very nice. I had not seen that one before.

That's actually a beautiful picture of things. I think it leads to a problem of evil though. Do you have a solution? — frank

Thank you. Because good (being) exists, distortions of good exist. As St. Augustine said, evil is not a positive thing in itself. It is a lack of the good. The good is a perfect symphony. Evil is disharmony. But evil cannot exist without the good, without being, which is God.

Could you guys share your philosophy of math with me? — frank

Numbers and the relationships between them are eternal truths. I'm sure God is aware of this. But math for God must be way beyond what we would even conceive of as math.

It is easy to create numbers.
Start with "/"
Iterate "//"
Reiterate "///"
etc "//////////////////..."

Partition each step:
/, //, ///,...
= 1, 2, 3,...
I'm sure God worked out this long before anyone else.

Once numbers exist mathematics (especially The Theory of Numbers) exists.
And once that exists, complexity exists.
Therefore God can be complex in terms of the contemplation of numbers.
And this answers Dawkins' assertion that God cannot be complex without a creator.
He can be complex by way of knowledge.
And once all this exists it is a matter of putting 'meat' on the abstract bones of mathematics.

Experience of reality in ordinary terms can awaken in our consciousness the mathematical order of reality because the world is intrinsically mathematical anyhow: induction awakens our powers of deduction. That, I think, is a big part of how science works.

One can show that if this is true for one shape it's true for any shape — InPitzotl

True. The spanner on the hypotenuse is equal to the sum of the spanners on the other two sides.

A-Theory: Time passes; the passage of time is real
B-Theory: Time doesn't pass; the passage of time is not real — Luke

Imagine a transparent ball rolling along a table. People live in the ball and look out at the surface of the table (time) going by. But all of the table is there all of the 'time'. Just a thought...

If time is real and the future did not happen yet then the earth of tomorrow (or the earth in one second from now) does not exist. Likewise with the past. The earth of one second ago does not exist. This means the earth, and everything else, must be recreated every nanosecond???

Religions are only echoes of the original revelations given to mankind. Through the years they have accumulated all kinds of secondary and sometimes dangerous teachings. Taoism is the essential teaching of religion; namely that there is a Way ("I am the way"). It is the way we practice religion that counts. Established religions are only different contexts in which people practice their faith. That is, what we believe is not very important. They way we live is.

Wisdom will never be able to keep up with knowledge. Knowledge grows exponentially, while wisdom grows incrementally at best. Thus, the gap between wisdom and knowledge (ie. power) grows ever wider, ever faster. — Nuke

So far anyhow, that's why we are in the fix we are in. Maybe the future will be better than this.

That's correct, but it's the 'you' that's supposed to tell me which perspective I am. — bizso09

Hardly possible. All possible relationships between people are infinite. Maybe that's what life is, infinite creativity.

Aah! Makes sense. Would the distinguished guests be keeping an ear out for strange sounds coming from the engine room? — TheMadFool

Not sure what you mean. What I'm saying is that science is about the nuts and bolts. But there's more to life and being than primitive truths. Of course it is possible for scientists to think in less primitive, reductive ways but I think that a reductive, scientific mind-set, by itself, cannot answer ontological questions convincingly.