Zeta-Flux Posted July 22, 2014 Posted July 22, 2014 It appears to me that mathematicians cheat by changing the definitions.How is this changing the definition? There are an unbounded, unmeasurable number of points. But apparently this isn't working, so just give me YOUR favorite example of something infinite (try to make it easy and explicit) and I'll try again.
ERayR Posted July 22, 2014 Posted July 22, 2014 Maybe it is the word "measure" which is throwing people off. If I was given a ball, there are many things about it I could measure. Its age, its weight, its volume, its electrical charge, the number of people who have touched it, the amount of hydrogen inside, etc... Similarly, there are things which possess infinite properties but we can still measure other aspects of them. For instance, the number pi possesses an infinite and unending decimal expansion, but the absolute value of the number is between 3 and 4, it is not rational (a fraction of integers), it satisfies some beautiful equations, etc... Likewise, there is something called cardinality, which is an important measure given to infinite (and finite) sets. You van I see it as simply recognizing and accounting for the shared infinite and finite aspects of the same object--not unlike the infinitely divisible, yet finite space between where a philosopher is standing and the wall mentioned in the OP. Thanks, -Wade Englund- I say potato you say potatoe.
Rob Osborn Posted July 22, 2014 Posted July 22, 2014 IN ANYTHINGMaybe it is the word "measure" which is throwing people off. If I was given a ball, there are many things about it I could measure. Its age, its weight, its volume, its electrical charge, the number of people who have touched it, the amount of hydrogen inside, etc... Similarly, there are things which possess infinite properties but we can still measure other aspects of them. For instance, the number pi possesses an infinite and unending decimal expansion, but the absolute value of the number is between 3 and 4, it is not rational (a fraction of integers), it satisfies some beautiful equations, etc... Likewise, there is something called cardinality, which is an important measure given to infinite (and finite) sets. The problem with cardinality as it applies to the infinite is that its an oxymoron to couple the two together. There is no set number of elements in something that is endless. Cardinality demands there be a set number of elements. In anything of finite number we can know and assign a cardinal value to it. But the same doesnt hold true for infinite things. We use natural numbers as a means to count things in multiples of tens. With this system its basically a repeating system of addition that just literally goes on an on forever. You could most definitely use this system of adding to count every single atom in the universe (if it were even possible). Think of it like the clicker guy that counts people as they walk through a door. His clicker only goes to a 1,000 and so whenever he gets to a 1,000 he makes a dash on his paper and begins again. He could go on doing this forever and ever counting to a 1,000, make a new dash on a paper and start over again on into infinity. These clicks- each one he makes represents the natural numbers- the symbol we use to count things. The uniqe thing about this system is that because it repeats over and over again into infinity you can literally count everysingle infinite thing there was to count and never run out of room to keep on counting them. So, when we peak of this system as having a cardinal size its quite an oxymoron because you cannot have a set number of this repeating process. there is no limit to its ability to just keep adding one more dash into infinity- it never ends- there is no set number of elements within it. To say that there is would be akin to having the clicker guy suddenly at some point run out of ability to click the clicker or run out of spots to make yet another dash. That is why it doesnt work. I can count in 1's, 10's, 100's, etc, on into forever and no matter what multiplication I am using it is just a repeating process that starts over each and everytime I count a new thing- it just never ends its a self repeating tool that allows us to count anything and everything without any worry of ever running out of its ability to count something new.
Rob Osborn Posted July 22, 2014 Posted July 22, 2014 Maybe it is the word "measure" which is throwing people off. If I was given a ball, there are many things about it I could measure. Its age, its weight, its volume, its electrical charge, the number of people who have touched it, the amount of hydrogen inside, etc... Similarly, there are things which possess infinite properties but we can still measure other aspects of them. For instance, the number pi possesses an infinite and unending decimal expansion, but the absolute value of the number is between 3 and 4, it is not rational (a fraction of integers), it satisfies some beautiful equations, etc... Likewise, there is something called cardinality, which is an important measure given to infinite (and finite) sets. We can look at things which are endless and marvel at that ability but we cannot however apply anything that is infinite and fully apply all of it to something- that doesnt exist. I could make a circle on a paper and then make another one three times bigger and look at each and marvel that each contain an infinite amount of points within the two circles. But the very moment I place it in a spot and define it in relation to the circle it becomes of finite value. I could also use these two circles to prove that two infinities are the same exact size even though one has a much larger surface area of points to use. This method- no matter how many points I made in the bigger circle it has the same exact relation in the smaller circle in relation to where it exists in the circle. Thus, no matter how many new points of reference I made in the bigger circle it correlates perfectly in the same position relatively speaking to the smaller circle. Thus, there is no point in the big circle where one could make a point that also wasnt in the smaller circle in relation to its perimeter.You can apply this logic to lines of different size, etc, etc. There is no measurement of two things both of infinite count- they always and must equal each other.
MormonFreeThinker Posted July 23, 2014 Posted July 23, 2014 Its not exact though. To get to "1" you have to cheat. The fact is you never will equal "1" by adding that way. It is not cheating, it's Calculus. It it is true that you cannot reach infinities, but you use infinities in Calculus to get solutions, and limits.
Rob Osborn Posted July 23, 2014 Posted July 23, 2014 It is not cheating, it's Calculus. It it is true that you cannot reach infinities, but you use infinities in Calculus to get solutions, and limits.You are right. I personally see infinities as being nothing more than just a means of saying it is endless, without a limit.
MormonFreeThinker Posted July 23, 2014 Posted July 23, 2014 (edited) You are right. I personally see infinities as being nothing more than just a means of saying it is endless, without a limit. Yes, infinities are endless, but you can use them in Calculus to get solutions. Even finite numbers like Graham's number are useful. Graham's number is a very big number, but it is useful, and you can Calculate the last digit, which is seven. Math is fun. Edited July 23, 2014 by MormonFreeThinker
Rob Osborn Posted July 23, 2014 Posted July 23, 2014 Its bothersome to me that set theory dealing with infnities is so accepted. Perhaps its the idea that infinities can come in different sizes that got everyone awestruck into belief. Now the whole world lays under the same old trick. Perhapswe really think time travel to the past is really possible too.The famous diagonal argument is perhaps a clever gimick but anyone with common sense can see its fault right off. It realy makes one wonder how it is ever possible to dupe the greater masses of the world for over a hundred years but then again,Darwin was also sold doing the same thing.
Nofear Posted July 23, 2014 Posted July 23, 2014 I'm gonna go with the mathematicians generally know what they are talking about and Rob Osborn's opinion about mathematics is woefully incorrect and misguided. More than that, I publicly ad hominem denounce his position as contrary to and damaging to the LDS tradition of intellectual pursuit. 1
Rob Osborn Posted July 23, 2014 Posted July 23, 2014 Suit yourself. Just ask yourself this- natural numbers is a system of counting that uses the count of 10 and just repeats indefinitely. Nothing is bigger in count than that ability. You can keep adding sets of 10 onto each other forever- its a system that has no limit to its count. How could a set of numbers ever be bigger than that?
wenglund Posted July 23, 2014 Posted July 23, 2014 Suit yourself. Just ask yourself this- natural numbers is a system of counting that uses the count of 10 and just repeats indefinitely. Nothing is bigger in count than that ability. You can keep adding sets of 10 onto each other forever- its a system that has no limit to its count. How could a set of numbers ever be bigger than that? If I have a pinky ring that is one eternal round (infinite), and were I also to have a big toe ring that also represents one eternal round (infinity), then assuming that my big toe is much larger than my pinky, one may reasonably conclude that the infinity of my big toe ring is bigger than the infinity of my pinky ring. Right? Thanks, -Wade Englund-
Nofear Posted July 23, 2014 Posted July 23, 2014 (edited) While there are different "sizes" (cardinalities) of infinities, unfortunately, wenglund, your analogy is incorrect. Admittedly infinities are really very non-intuitive and hard to understand... http://ed.ted.com/lessons/how-big-is-infinity Edited July 23, 2014 by Nofear
Rob Osborn Posted July 23, 2014 Posted July 23, 2014 Theres no such thing as infinities of different sizes. Something which is infinite means it is without limit to size. You thus cannit measure something that has no end.
Nofear Posted July 23, 2014 Posted July 23, 2014 (edited) You can say that all you want, but in is in contradiction to pretty much every educated mathematician and pretty much anybody else who looks closely at the issue. See link to article above. Instead of spending time explaining I'll simply lazily use appeal to authority as my argument. It's ok to be wrong. Bigger the individual who'll admit it (double edged sword such that it is). Postscript: Anyway, that's my brief stop by this discussion. Not one that I'm really going to follow up with. Edited July 23, 2014 by Nofear
thesometimesaint Posted July 23, 2014 Posted July 23, 2014 (edited) Theres no such thing as infinities of different sizes. Something which is infinite means it is without limit to size. You thus cannit measure something that has no end. In numbers there is. There is an infinite number of decimal points between 0 and 1, as well as whole numbers between 0 and well infinity. The minute it is measured it is no longer infinite. Scale of universe. Edited July 23, 2014 by thesometimesaint
Rob Osborn Posted July 23, 2014 Posted July 23, 2014 In numbers there is. There is an infinite number of decimal points between 0 and 1, as well as whole numbers between 0 and well infinity. The minute it is measured it is no longer infinite. Scale of universe. And you could use the natural numbers to count everyone of those infinite decimals. The point being that there is no such a thing as running out of something that doesnt have an end. 1
Rob Osborn Posted July 23, 2014 Posted July 23, 2014 You can say that all you want, but in is in contradiction to pretty much every educated mathematician and pretty much anybody else who looks closely at the issue. See link to article above. Instead of spending time explaining I'll simply lazily use appeal to authority as my argument. It's ok to be wrong. Bigger the individual who'll admit it (double edged sword such that it is). Postscript: Anyway, that's my brief stop by this discussion. Not one that I'm really going to follow up with.And thus the reason why the masses are duped- they cant see it through themselves. Ask yourself this one little thing- is it posible that the repeating set of 10 and the addition of those sets ends after some point?
thesometimesaint Posted July 23, 2014 Posted July 23, 2014 And you could use the natural numbers to count everyone of those infinite decimals. The point being that there is no such a thing as running out of something that doesnt have an end. I said nothing about running out of infinity. However we do live on a finite planet.
thesometimesaint Posted July 23, 2014 Posted July 23, 2014 And thus the reason why the masses are duped- they cant see it through themselves. Ask yourself this one little thing- is it posible that the repeating set of 10 and the addition of those sets ends after some point? It never ends. But at some point its practicality in our everyday lives to us mortals becomes questionable.
MormonFreeThinker Posted July 23, 2014 Posted July 23, 2014 (edited) And you could use the natural numbers to count everyone of those infinite decimals. Rob, I think everyone agrees with you, you can't count infinity because it never ends, you will never reach it. I think you are missing the point, you can use infinities to do math. 1/2 + 1/4 + 1/8+ 1/ 16 ... to infinity = 1, that is Calculus. The limit of 1/x as x approaches infinity, the answer is 0. You can use an infinite amount of rectangles to find the exact area under a curve. Calculus is science, and Elder Oaks said, "Latter-day Saints believe in applying the best available scientific knowledge and techniques" Astronomers use Calculus to study the universe, Elder Richard Scott said, "We can see the scientific method has brought about an extraordinary expansion of our understanding as the Lord has inspired gifted men" Edited July 23, 2014 by MormonFreeThinker
wenglund Posted July 23, 2014 Posted July 23, 2014 While there are different "sizes" (cardinalities) of infinities, unfortunately, wenglund, your analogy is incorrect. How so? Thanks, -Wade Englund-
Nofear Posted July 23, 2014 Posted July 23, 2014 How so? Thanks, -Wade Englund-For the same reason the cardinality of odd integers is the same as the cardinality of all integers (both even and odd). The Ted ed video that I linked may help.
Rob Osborn Posted July 23, 2014 Posted July 23, 2014 Rob, I think everyone agrees with you, you can't count infinity because it never ends, you will never reach it. I think you are missing the point, you can use infinities to do math. 1/2 + 1/4 + 1/8+ 1/ 16 ... to infinity = 1, that is Calculus. The limit of 1/x as x approaches infinity, the answer is 0. You can use an infinite amount of rectangles to find the exact area under a curve. Calculus is science, and Elder Oaks said, "Latter-day Saints believe in applying the best available scientific knowledge and techniques" Astronomers use Calculus to study the universe, Elder Richard Scott said, "We can see the scientific method has brought about an extraordinary expansion of our understanding as the Lord has inspired gifted men"Just making clear that there is no such a thing as one infinity being dmaller or larger than another infinity.
Ahab Posted July 23, 2014 Posted July 23, 2014 Theres no such thing as infinities of different sizes. Something which is infinite means it is without limit to size. You thus cannit measure something that has no end.Okay now you're just not thinking clearly, or at least not when you said that.Consider how there are an infinite number of persons who are the kind of being our Father is, and also an infinite number of chickens.At full maturity, our Father is bigger in size than a chicken.
MormonFreeThinker Posted July 23, 2014 Posted July 23, 2014 Okay now you're just not thinking clearly, or at least not when you said that. Do you believe in the Big Bang Theory?
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