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If a liar that always lies tells you he's lying... Would you believe him?

 

Yes

 

 

 

Meh. I don't remember the exact thing, but it was something like that. BUT, if you believe him, it means he wouldn't be lying, which wouldn't make him a liar.

 

Can't you believe a lie?

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If a liar that always lies tells you he's lying... Would you believe him?

 

Yes

 

 

 

Meh. I don't remember the exact thing, but it was something like that. BUT, if you believe him, it means he wouldn't be lying, which wouldn't make him a liar.

 

Can't you believe a lie?

 

 

 

You made me remember it! If a liar tells you he's lying, is he telling the truth?

 

 

 

(I have no idea how your post reminded me of it, but it did one way or the other)

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A common mistake among students just learning the calculus is a confusion between a quantity being allowed to approach infinity and actual instances of infinity. For example: It is incorrect to say that 0.333... is not equal to 1/3. The common error is to assert that "as the threes go on and on, you get closer and closer to one third, but you can't actually get there since the threes would have to be infinite."

 

 

 

The perpetrator of this error is assuming that the threes are not already infinite. However, the expression 0.333... indicates that an infinite number of threes already exist, as implied by the ellipsis. 0.333... does not need an observation or anyone's permission to have an infinite number of threes. It is neither necessary nor proper to speak of the value "approaching" some other value. The value of 0.333... is concrete. If one is thinking of a number that begins 0.333 that ends at some arbitrary point, and imagining adding 3s one by one, that person is not thinking of the number 0.333... at all.

 

 

 

It is only proper to speak of the value of a formula, sequence, or series approaching a given value in the context of limits. "0.333..." does not require or imply that the use of a limit is appropriate. It is proper to say that 0.333... is exactly equal to 1/3. By extension, 0.666... does not have a seven "at the end", nor is 0.999... "almost but not quite equal to one." Novices to the field of epsilontics will claim that 0.999... "can be made as close to 1 as you like, but will never equal 1." They are incorrect. The value of 0.999... is well-defined, equal to 1, and not subject to change due to observation.

 

 

 

Hope that helps some of you. It's a small bit of how I explain infinity to my pre-cal students.

 

 

 

 

 

And my favorite paradox is not so much a paradox as an exercise in counterintuitive thought: At exactly 7 am one morning, a hiker begins to ascend a mountain trail. The hiker does not necessarily move at a constant speed, and may stop to rest, but never backtracks along the path. Sometime later, the hiker reaches the top of the mountain and sets up camp for the night. At exactly 7am the following morning, the hiker begins to descend the mountain by the exact same path. Again, the hiker may travel at any speed, even stopping, but does not backtrack.

 

 

 

The question: is it impossible, possible, or necessary that there should exist one or more points along the trail that the hiker passes at exactly the same time of day coming down the mountain on day 2 as going up the mountain on day 1? If it is possible or necessary, how many points meet this requirement?

 

 

 

Good luck with the reasoning.

 

Mensch

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The question: is it impossible, possible, or necessary that there should exist one or more points along the trail that the hiker passes at exactly the same time of day coming down the mountain on day 2 as going up the mountain on day 1? If it is possible or necessary, how many points meet this requirement?

 

 

 

are you asking for the total number of points that can exhibit this or the most points in a single trip?

 

 

 

I believe there are an infinite amount of points that could have this occur, the hiker could remain at the top of the mountain till one minute before the time of a point then run down to it since we arent putting a limit on his speed. So any point on the trail excluding the beginning and end point could be a point of occurence and since there are an infinite amount of points between any two different points the answer is infinity

 

 

 

As for how many such points in a single run...

 

 

 

hmm, I would have to say a single point, since the return distance is decreasing while the going up line is increasing they could meet anywhere but once they connect they will have gone past each other.

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Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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Can omniscient God, who

 

Knows the future, find

 

The omnipotence to

 

Change His future mind?

 

 

 

that is kind of hard to understand but if were assuming god has infinite power then he can at any time change whatever he wants to determine the future. Think of it as being in a room full of buttons each of which changes the color of light coming from a bulb. At any time you can change or not change the bulb color(symolyzing reality) through your power to push buttons(god influencing or not influencing reality)

awteno.jpg

Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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you have missunderstood the paradox. If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means he can't change his mind about his intervention, which means he is not omnipotent.

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you have missunderstood the paradox. If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means he can't change his mind about his intervention, which means he is not omnipotent.

 

 

 

I could walk into a store knowing im going to buy a box of twinkies, I still buy them of my own free will.

awteno.jpg

Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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You are completely missing the point. Although you intend to go in and by your confectionary, you can not know the future - an event may occur that prevents you from doing this, however God does not suffer these constraints. God 'knows' the future.

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if nothing can interfere with god then anything he knows he will choose he has already chosen and knows will happen.

 

 

 

Imagine Im watching myself on a tv that has a two second time shift into the future. I could be getting dressed, see myself put my belt on then still choose to put the belt on next

awteno.jpg

Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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if nothing can interfere with god then anything he knows he will choose he has already chosen and knows will happen.

 

 

Yes, you are right. If he was truly omnipotent, surely he would have the power to change this decision?

 

 

 

yes, but since an omnipotent being can make what it deems the best decision in a time interval of 0 he has already made the "correct" decision and then can forsee what he has already chosen after he has chosen it. If you claim god has no limits then it is logical he can do things while negating our convention of time.

awteno.jpg

Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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...The question: is it impossible, possible, or necessary that there should exist one or more points along the trail that the hiker passes at exactly the same time of day coming down the mountain on day 2 as going up the mountain on day 1? If it is possible or necessary, how many points meet this requirement?

 

 

 

Good luck with the reasoning.

 

Mensch

 

Hmm, after drawing a little graph it seems that it's necessary that he'll reach such a point, and not more than one.

 

My reasoning is: We lay a time-path graph. Day 1 is always an ascending slope (as he is climbing up and never goes back), and day 2 is always descending. Because the starting and ending points are the same (but reversed), the paths will always cross once, forming something like an 'X'-

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I dont think this is really a paradox, more like a joke/riddle.

 

 

 

Picture a house shaped like a 3 sided pyramid. A rooster is standing at the very top, and lays an egg. The wind is blowing 25 km/h west. which way does the egg fall?

 

 

 

[hide=Answer]Roosters dont lay eggs :twss:[/hide]

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I dont think this is really a paradox, more like a joke/riddle.

 

 

 

Picture a house shaped like a 3 sided pyramid. A rooster is standing at the very top, and lays an egg. The wind is blowing 25 km/h west. which way does the egg fall?

 

 

 

[hide=Answer]Roosters dont lay eggs :twss:[/hide]

 

Thats so easy.

 

:lol:

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I dont think this is really a paradox, more like a joke/riddle.

 

 

 

Picture a house shaped like a 3 sided pyramid. A rooster is standing at the very top, and lays an egg. The wind is blowing 25 km/h west. which way does the egg fall?

 

 

 

[hide=Answer]Roosters dont lay eggs :twss:[/hide]

 

Thats so easy.

 

:lol:

 

 

 

Its alot easier in writing. Plus, tipiters a genuises. Try it out on some real life friends, you'll be surprised :P

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...The question: is it impossible, possible, or necessary that there should exist one or more points along the trail that the hiker passes at exactly the same time of day coming down the mountain on day 2 as going up the mountain on day 1? If it is possible or necessary, how many points meet this requirement?

 

 

 

Good luck with the reasoning.

 

Mensch

 

Hmm, after drawing a little graph it seems that it's necessary that he'll reach such a point, and not more than one.

 

My reasoning is: We lay a time-path graph. Day 1 is always an ascending slope (as he is climbing up and never goes back), and day 2 is always descending. Because the starting and ending points are the same (but reversed), the paths will always cross once, forming something like an 'X'-

 

 

 

Same line of thinking I was using

 

 

 

do you also agree that since speed can vary the intersection point could be anywhere between the beginning and the end?

awteno.jpg

Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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Here is another one:

 

 

 

A man is a condoctor, who is payed very little. He had to steal to feed his family, and is caught and sentanced to death (harsh, much?) The day before his executtion, he is allowed to eat whatever he wants. He eats: Turket (white meat), pulp-free orange juice, and a corn on the cob with butter. That evening, in the electric chair, there is a surge of power when it is turned on. So, they do the same the next day. He gets another "anything you want" meal, and orders the same food. Again, the power surges, and he lives. Why isn't he being killed?

 

 

 

Ill let you guys figure it out.

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Im going to guess the answer is based on the fact he is a conductor(pun on electric conductor) and if it is his job he clearly has natural immunity.

 

 

 

Damn it. :wall:

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Im going to guess the answer is based on the fact he is a conductor(pun on electric conductor) and if it is his job he clearly has natural immunity.

 

 

 

Damn it. :wall:

 

 

 

:twisted: :lol: :lol: :twisted:

 

 

 

if it makes you feel better I almost missed it

awteno.jpg

Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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if nothing can interfere with god then anything he knows he will choose he has already chosen and knows will happen.

 

 

Yes, you are right. If he was truly omnipotent, surely he would have the power to change this decision?

 

 

 

yes, but since an omnipotent being can make what it deems the best decision in a time interval of 0 he has already made the "correct" decision and then can forsee what he has already chosen after he has chosen it. If you claim god has no limits then it is logical he can do things while negating our convention of time.

 

You are over-complicating it, and do not appear to understand... This paradox involves an infinite regress - the answer to a question raises a prior question, and so on ad infinitum. Therefore, logically omniscience and omnipotence are mutually incompatible.

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An ancient device lets us see through walls. What is this known as?

 

 

 

[hide=]Windows[/hide]

 

 

 

I know, another terrible riddle by kirby :|

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Hmm, after drawing a little graph it seems that it's necessary that he'll reach such a point, and not more than one.

 

My reasoning is: We lay a time-path graph. Day 1 is always an ascending slope (as he is climbing up and never goes back), and day 2 is always descending. Because the starting and ending points are the same (but reversed), the paths will always cross once, forming something like an 'X'-

 

 

 

Same line of thinking I was using

 

 

 

do you also agree that since speed can vary the intersection point could be anywhere between the beginning and the end?

 

 

 

 

 

Well done. Exactly one point, position indeterminable. The way it was explained to me was by analogy to racing games. Imagine the hiker's "ghost run" from day 1 was coming up the mountain on day 2. At exactly one point, the hiker and the ghost would pass each other.

 

 

 

You guys ever heard of the paradox of the unexpected hanging?

 

 

 

Mensch

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