Re: curve that’s been discussed over the last few posts.
The integral of 1/x^(1+n) where n > 0 converges. When n = 0, < 0 it diverges.
You’re probably talking about 1/x^2. The value of x can never get large enough such that this is zero, yet the integral converges. If I’m correct a good way to think of it as a two dimensional extension of Zeno’s paradox*: Where the distance between the function and the Y axis is the distance between the rabbit and the carrot, yet the line continues forward in the X axis to infinity.
*If a rabbit is 1 foot away from a carrot, and moves forward such that it halves the distance, how does it ever reach the carrot?
yeah
inverse exponential
hahaa
for my argument I was actually planning on drawing a parallel from this mathmatical thought experiment exctly to Zeno’s philosophical paradoxes (which divide up space or time into infinitesimally small units in order to contradict reason) to show that even paradoxes which seem to arise via mathematics are not a failure of math, rather they are an artifact of the human element.
but something went awry
hahaa
No. Your statement was demonstrated to be logically absurd. Assuming the conclusion that humanity is capable of perfection doesn’t then mean that your original statement of humanity being incapable of perfection is true because they are contradictory statements.
You don’t define premises, you define words. You STATE premises. If you assume that you can never fully analyze all human actions that have ever occurred, it doesn’t follow then that we have no premises to create a conclusion from … especially since you based your original conclusion on the premise that humanity is incapable of producing anything perfect. Granted it was false, but was still a conclusion.
No. Your statement was already demonstrated to be logically absurd. It would be considered a poor argument.
Given that you have demonstrated both poor math and poor reasoning skills, it is pretty obvious that you really aren’t good at thinking or making a case for things. All you can do is misuse terminology that you are incapable of understanding (see I easily found a human action that cannot be improved) in a way that only sounds intelligent to you. Now I know you’ll probably say something like “you misspelled quantum, so your comments are automatically wrong” but in all honesty, you really are a prime example of why algebra should be emphasized in a grade school curriculum. Do we really want our high-school/college graduates to enter the real world thinking that 4-1 depends on quantum mechanics?
I’m sorry but your post is invalidated by the fact you misspelled “were.” /sarcasm
Guys help me out here. I have a problem. I’m going to pay a guy to do something, and he says he wants $20, but I don’t know how to pay him.
I have a $20 bill $10 bill, 2 $5 bills, and at least 10 $1 bills. Before coming to this thread I’d have just given him the $20 bill and called it a day, but I’m just not sure. If a guy asks for $20, and I give him $20 is that exactly how much he asked for or not? Also how do I check the quantum flux of my macroscopic $20 bill to see if it will be acceptable? Also should I give him the 10, 5, and 5? Is that 20? Or is it 19.9999999999. If it’s 20.000001 How do I get the fraction of a penny for change back? If I give him more bills that’s more quantum flux to worry about but if one of them does go through some odd change, at least that’ll be less money to worry about losing.
math is imperfect and cannot model a real dollar, because each dollar is actually an infinite amount of dollars across an infinite number of parallel universes followed by an infinite number of zeroes after the decimal point. therefore there are bound to be rounding errors, since adding or subtracting from infinity results in more infinity.
Heave you heard of the internet, after school, lunch, life? Communication is doing fine. I don’t see how this vision of pitch perfect conversation (and I suppose verbal information exchange) is actually doing anything academic (and personally i think its vague and do-nothing).
The point is to output smart critically thinking people; which we don’t do. Bad math teachers/parents caused this problem and now we have a generation who do not even know how to think about math. They are numerically illiterate.
Education is what is left after you’ve ‘learned’, so I would say vast swaths of people are just too uneducated to speak on the issue. You hear a lot about how we will never be using this particular subset, or how its useless due to this unsolved issue i found on Wikipedia but very little about how it keeps your mind actively thinking in abstract ways and that there’s something to be said for being able to grab a book, read it, and execute what you’ve learned (rather than rotely remembering what happened in 1492 followed by a lot of factoids that might turn the whole event on its head at a cocktail party). There is very little in the pedestrian world about Maths deep relationship to creation. If you want to really do something useful (or fail trying) then you need to math up.
Don’t be ridiculous. By the fundamental theorem of Matriarchal mathematics, 1 = infinity. So you wouldn’t have one island, you have infinite islands.
Btw, I just found an amazing corollary guys!
1 = infinity iff 0 = 1 – infinity
infinity = infinity + 1
so 0 = 1-1 – infinity
so 0 = -infinity
multiply by -1 on both sides…
so 0 = infinity
and infinity = 1
so 0 = 1 = infinity
So from nothing emerges something.
There’s no paradox with Gabriel’s Horn. You can never actually make a physical version of it, so I don’t see what’s so strange about infinite surface area and finite volume for an impossible object. It’s like saying the integers are a paradox because there are more integers than atoms in the universe. So what?
As for Zeno’s paradoxes, I think the point goes over most people’s heads (probably mine too, since I never really made an effort to go through them). As far as I know, he tried to come up with thought experiments to show that infinitely divisible, continuous space and discrete space both lead to contradictions. He didn’t really think that he couldn’t walk to a wall lol. If you use an infinite series to “prove” that you can reach a wall, like so many proud calc 1 textbook authors, instead of just walking to it, then you just look stupid.
Lastly, with all this talk of “infinity”, it’s kind of funny that calculus actually avoids infinity like the plague. Try to find a mention of it in any definitions. You’ll find a lot of absolute values and deltas and epsilons and “for all n>N”, but any use of infinity is informal or as a notational convenience.
It doesn’t avoid infinity, rather it doesn’ t use infinity in the same way the average calculus student thinks about it. You do see the formal definition of infinity in upper level math courses as you gave, but they still talk about infinity. They just word it as “divergent” or some other term. The problem is people love to see infinity as any other number when it is only a concept.
Its like an infinite series doesn’t really exist, but what i means is that if we continue the series we get closer and closer to the desired value. It just means “as large as we wish to make it”
Just so people can be aware of something to help them visualize things like 1/x:
I popped up the interface and typed in:
x = var(‘x’)
h=1/x
–> Create a symbolic variable and create a function h(x) = 1/x
h.integral(x,1, infinity)
ValueError: Integral is divergent.
L = [[a,1/a] for a in range(1,100)]
–> Create a series of values for 1/x for x=1 to 100
That’s basically what I was getting at. I just wanted to make sure people realized that when they say “adding infinitely many infinitely thin rectangles”, that’s just a convenient (and extremely confusing unless you’re careful) way to express a Riemann sum. What they’re really doing is adding a finite number of rectangles and getting close enough, but still within a finite distance, to some number*. Pretty clever stuff, which is why it took about 200 years to give calculus a solid theoretical foundation.
*Well, what they’re really doing is using the fundamental theorem of calculus or a computer, but we’ll pretend for now.
Perelman could have, but he’s such a badass he refused his million dollar prize. Grothendieck is also a total badass who left math and now lives as some kind of hermit lol.
It is only an impossible object becuase presumably infinite anything (eg: surface area) exists only in theory, (so the word ‘impossible’ in the ablove sentence is kindof redundant) Right?
If you agree with that reading, you seem to be saying that becuase infinity doesnt exist in reality, anything goes (‘what’s so strange’).
In other words, you hold the position that any thought experiment assuming it does exist in reality is pointless?
That sounds like an argument against calculus
no?
I dont see how that is a pradox. Perhaps only if you believe in a religion where that the number of atoms in the universe dogmatically constitutes the greatest possible number. Does anyone subscribe to that?.
Or maybe only if you believe that theory and reality must always overlap would you believe that constitutes a paradox; which is weird because in your first quote above you seem to be implying exactly that; that they must not be distinct or else you are wasting time even thinking about it.
algebra is used in everyday life. when you have a group of quantities that are related, but at least one of those quantities is unknown, algebra will explain the relationship in between those quantities, and therefore the solution to the unknown. a lot of it is actually common sense and language, not numbers.
