A math Problem

[Grumpy Santa]

yes, the fact that the real numbers are infinite, does not prove that I could have typed any number,.................................as mentioned before it would have been impossible for me to type a number with trillions of digits because I don't have enough time and my computer does not have enough memory to support such a large number

6.0236633 * 10^5000^5000

 

[leroy]

I could have not typed a number with trillions of digits because long before that I would have died

Setting aside that this derail is entirely irrelevant to the question at hand, which concerns the general case of selecting a number at random, this is still wrong, because it's trivial to write a number down with trillions of digits. That's what exponents are for.

All utterly without relevance to the discussion, though, because we're not talking about what Leroy can select, because that's probably limited to 2 digits or fewer.

yes it is relevant because your whole argument is based on the assumption that it is possible to type (or think about) any real number. ................there are numbers that are impossible to think about or type because they have so many digits.



ok if you use exponentials you can write a number with trillions of digits, but even with exponentials you will get to a point when a number is so large that it would be impossible to type it (given my limited time, limited computer memory, etc.)




hackenslash give up, selecting a random number is not an event with 1/ infinite possibilities there is always a limited amount of numbers to choose from,

 

[leroy]

yes, the fact that the real numbers are infinite, does not prove that I could have typed any number,.................................as mentioned before it would have been impossible for me to type a number with trillions of digits because I don't have enough time and my computer does not have enough memory to support such a large number

6.0236633 * 10^5000^5000

ok, simple change a number with trilions of digits for a number with 10^1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 digits, it is still a fact that the options are finite, there is only a finite amount of numbers that can be typed in a computer.



not to mention that hackenslash is basing his argument on the assumption that all numbers have the same probability of being selected, which is wrong or at least he has not proved that assumption

 

[leroy]

If you recognize the random number 4287 as being one of an infinite set, then by definition he's correct.

.

No that is exactly that part that I don't grant 4287 belongs to the set of real numbers that can be typed in a computer ................which is a finite set


for example assuming that I will only live 100 years from now, assuming that theie is the only barrier that limits my options, the set will only include numbers that are possible to write in 100 years, even with exponentials, the set would still be finite.


I would also say that 4287 or any other small number with few digits is more likely to be typed than a number with millions of digits .............not all the numbers have the same probability of being typed.

I am presumible more likely to waste a few seconds writing a random number than wasting 50 years



So in short, the set of real numbers is infinite, but the set of numbers that are possible to type in a computer is finite.......agree?

 

[Grumpy Santa]

6.0236633 * 10^5000^5000

ok, simple change a number with trilions of digits for a number with 10^1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 digits, it is still a fact that the options are finite, there is only a finite amount of numbers that can be typed in a computer.



not to mention that hackenslash is basing his argument on the assumption that all numbers have the same probability of being selected, which is wrong or at least he has not proved that assumption

He's right though if you're talking about a pure random sampling from that infinite set. You're talking about two different sets of numbers here, an infinite one and a very big yet finite one that you seem to be describing.

Do you acknowledge that you're not talking about the same set of numbers that he is?
Do you understand that infinity is not a number, but instead is a concept?
Do you understand that any number divided by infinity is, by definition, zero?

By the way, you example, where you're going out to trillions of numbers, is actually going harm. You need to look up the concept of "effectively negligible". Things with fantastically small but positive probabilities are said to be effectively negligible, or effectively zero.

 

[Dragan Glas]

Greetings,

The chance of you picking a number is 1 in infinity.

This is simply a fact.

No-one knows whether you're going to limit yourself to a certain number of digits or not when you choose to type a number.

You could have written 4287^7824 - which is a real number capable of being typed into your computer.

Kindest regards,

James

 

[leroy]

Do you acknowledge that you're not talking about the same set of numbers that he is?
.

yes we are talking about the same set of numbers HWN and I are both talking about the set of numbers that can be typed in a computer (given limited memory, limited time etc.) this set is big but finite. ............agree


hackenslash was talking about the set of numbers that can be selected (he didn't specified, if he is talking about selected by a brain, or by a computer, or a calculator...) but in any case the set in finite ..............agree

 

[Grumpy Santa]

If you recognize the random number 4287 as being one of an infinite set, then by definition he's correct.

.

No that is exactly that part that I don't grant 4287 belongs to the set of real numbers that can be typed in a computer ................which is a finite set

Well, since you're being completely dishonest and cutting out the part where I was saying you were right I'm not going to give you this one. It is a fact that 4287 is indeed a part of an infinite set and under that understanding he's correct. This is a fact, Leroy. Quit jerking around this.

I also acknowledged that you're using it as a part of a finite set, and that changes things. However depending on the size of your finite set as a whole you could still be dealing with what's known as an effectively negligible probability, or a zero probability.

So, if you're going to at least simulate being completely honest, state the size of the set you're using with regards to coming up with a random number. Look, I and everyone else here understands where you've shifted your argument... a person is most likely to pick a random number from within a very narrow range. But you're using that to talk past the argument while ignoring simple facts.

 

[Grumpy Santa]

Do you acknowledge that you're not talking about the same set of numbers that he is?
.

yes we are talking about the same set of numbers HWN and I are both talking about the set of numbers that can be typed in a computer (given limited memory, limited time etc.) this set is big but finite. ............agree


hackenslash was talking about the set of numbers that can be selected (he didn't specified, if he is talking about selected by a brain, or by a computer, or a calculator...) but in any case the set in finite ..............agree

You're being aggravatingly dishonest Leroy. You ignored these:

Do you understand that infinity is not a number, but instead is a concept?
Do you understand that any number divided by infinity is, by definition, zero?

Shameful. Acknowledging these doesn't harm your argument, it just helps show where you're talking past each other, that's all.

If you look at Dragon's last reply it's clear that many are talking about an infinite set of numbers, be honest and admit that. I understand that you're talking about a finite set.

C'mon man.

 

[leroy]

Greetings,

The chance of you picking a number is 1 in infinity.

This is simply a fact.

No-one knows whether you're going to limit yourself to a certain number of digits or not when you choose to type a number.

You could have written 4287^7824 - which is a real number capable of being typed into your computer.

Kindest regards,

James

well then prove that it is possible to type ANY real number and you have to prove that any number has the same probability of being typed ..........


o wait I forgot, you aee an atheist and therefore you are not suppose to prove anything,

 

[leroy]

You're being aggravatingly dishonest Leroy. You ignored these:

Do you understand that infinity is not a number, but instead is a concept?
Do you understand that any number divided by infinity is, by definition, zero?

.

yes I understand and grant both points.


however the set of numbers that can be typed in a computer is still a finite set, even after granting those 2 facts......................agree? yes o no?

 

[Grumpy Santa]

You're being aggravatingly dishonest Leroy. You ignored these:

Do you understand that infinity is not a number, but instead is a concept?
Do you understand that any number divided by infinity is, by definition, zero?

.

yes I understand and grant both points.


however the set of numbers that can be typed in a computer is still a finite set, even after granting those 2 facts......................agree? yes o no?

My apologies, but with the use of exponents and other algorithms to represent numbers that's actually no.

I know, that's picking nits, and you're actually approaching this wrong. Forget about the capabilities of the computer, it's irrelevant. For what you're trying to explain you need to consider the capabilities of the average human mind and the likeliness that the average person won't come up with Avagadro's number to the square of Pi at random but more likely a positive integer less than 10,000. There will be exceptions of course.

So, it's true that if a number were selected at random (just purely random, not by a person) then that number would be selected from an infinite set and would, by definition, have had a zero probability of being selected. This is simply a fact, please admit it.

You're saying, however, that a random number chosen by a human mind as a processor will come from a finite set which is bound by the imagination and processing of that individual mind, which will vary. That's my understanding of your argument, and if so, it's correct. There's a limit to what the human mind can simply comprehend. We evolved with the capacity to quickly and easily grasp concepts and quantities that helped with our survival, and those numbers are much closer to zero than not.

So two things are effectively demonstrated here... yes, zero probability events can indeed happen (and do all the time), and the human mind is unable to comprehend infinity and incorporate that concept in the random choosing of numbers.

 

[Dragan Glas]

Greetings,

Greetings,

The chance of you picking a number is 1 in infinity.

This is simply a fact.

No-one knows whether you're going to limit yourself to a certain number of digits or not when you choose to type a number.

You could have written 4287^7824 - which is a real number capable of being typed into your computer.

Kindest regards,

James

well then prove that it is possible to type ANY real number and you have to prove that any number has the same probability of being typed ..........

What's to stop you typing any real number?

As already noted, using exponents, you can type any number you want.

If you're simply claiming that you didn't think of using exponents when you typed a number, that doesn't change the fact that the chance of you typing a number is 1 in infinity. If you're excluding the use of exponents, then that's a limit you're placing on yourself - it's not an absolute limit.

You could even have typed 4287^infinity or infinity^4287 - which is larger?

There are no limits to the numbers that you - or anyone - can type into a computer.

o wait I forgot, you aee an atheist and therefore you are not suppose to prove anything,

Being sarcastic is not going to help you win this argument, leroy.

You didn't think of using exponents, did you? You were only thinking of having to type out numbers "long-hand".

Kindest regards,

James

 

[leroy]

My apologies, but with the use of exponents and other algorithms to represent numbers that's actually no.

nope, even with algorithms, exponentials, decimals etc. the options are still finte ..........and I can prove it if you ask me to.

. For what you're trying to explain you need to consider the capabilities of the average human mind and the likeliness that the average person won't come up with Avagadro's number to the square of Pi at random but more likely a positive integer less than 10,000. There will be exceptions of course.

yes and you ll be surprised to see that most people in this forum would disagree with this statement, thy would argue that Avagadro's number to the square of Pi has the same probability of being selected than a positive integer less than 10,000,

So, it's true that if a number were selected at random (just purely random, not by a person) then that number would be selected from an infinite set and would, by definition, have had a zero probability of being selected. This is simply a fact, please admit it.

NO, that is my main point of disagreement, humans computers robots and calculators would also be selecting from a finite set, for example my hand calculator can only select numbers with 12 digits or less.

. There's a limit to what the human mind can simply comprehend. We evolved with the capacity to quickly and easily grasp concepts and quantities that helped with our survival, and those numbers are much closer to zero than not.

and the same is true for calculators robots, computers etc. they also have limits

 

[leroy]

well then prove that it is possible to type ANY real number and you have to prove that any number has the same probability of being typed ..........

What's to stop you typing any real number?

/quote]

many things stop me, time would be an example, even with exponents logarithms decimals or whatever, there is still a limited amount of numbers that can be typed.

 

[Dragan Glas]

Greetings,

well then prove that it is possible to type ANY real number and you have to prove that any number has the same probability of being typed ..........

What's to stop you typing any real number?/quote]
many things stop me, time would be an example, even with exponents logarithms decimals or whatever, there is still a limited amount of numbers that can be typed.

You can represent any number using exponents - and they don't take that long to type.

Kindest regards,

James

 

[leroy]

You can represent any number using exponents - and they don't take that long to type.

maybe you can type any number using exponentials, but there will be a point where the exponential is so big, with so many digits, that it would be imposible to type it in a life time

 

[Grumpy Santa]

So, it's true that if a number were selected at random (just purely random, not by a person) then that number would be selected from an infinite set and would, by definition, have had a zero probability of being selected. This is simply a fact, please admit it.

NO, that is my main point of disagreement, humans computers robots and calculators would also be selecting from a finite set, for example my hand calculator can only select numbers with 12 digits or less.

Leroy, please pay attention. I didn't say a computer, calculator, etc. I said a purely random selection.

 

[leroy]

Leroy, please pay attention. I didn't say a computer, calculator, etc. I said a purely random selection.

And who is making the random selection? a computer? a robot? a human?



lets see if we can agree with this statement


If one select a random number from the set of real numbers, the probabilities of selecting a particular number would be 1 / Infinity (or Zero) but there is not an existing mechanism (computer, human, robot etc.) that can do such selection, any known mechanism would select from a finite set of numbers. (for example my hand calculator could only select from numbers that have 13 or less digits which is a finite set. )


hopefully you agree and we can close this conversation, if you disagree well I would not have anything else to add,



any comment that is unrelated to the original topic of this tread will be ignored, if you what to maintain a conversation on this topic please open a new thread

 

[he_who_is_nobody]

which of these 3 points do you find controversial?



1 that I will only exist for a limited amount of time, and therefore it would be imposible for me to type a digit with trillions of digits?

2 that there is a finite amount of real numbers that have between 1 and 1 trillion digits?


3 that 1 divided by a finite number is NOT ZERO

I find none of those controversial, I do, however, wonder why you are talking about only trillions of digits in your second point. I believe Dragan Glas is correct.

However, it also seems that you agree that the real numbers are infinite.

leroy[/url]"]yes, the fact that the real numbers are infinite...

leroy[/url]"]So in short, the set of real numbers is infinite...

Thus, back to my equation and I will make it big for you, since you seemed to have missed it the last time.

X/(real numbers)(one's time)(one's memory)(y)(z)....

What is wrong with that equation? Would that not be how we determine the odds of picking a number at random? Remember, we are talking about the odds. If that is not how we would calculate the odds, please show us how.