It's is a personal Philosophy based on Christian views (not written here)... So or it belongs to General Philosophy or maybe to Religion...
Sure supreme dictator!...err... I mean... moderator...should I have closed your thread instead of moving it to an appropriate forum?
Sure supreme dictator!...err... I mean... moderator...
Originally posted by TruthSeeker
Think about it honestly...![]()
Go look at a basic calculus textbook to see why zeno's paradox isn't really a paradox. Zeno's paradox relies on the assumption that the sum of an infinite number of numbers must always be infinite, which is incorrect.Originally posted by notme2000
Go look up the Zeno's Paradox thread to see why this is not true. What is half a second? And half of that? And half of that? So you see it can go in to infinity and there is no set unit to measure time by.
Ok, I know next to nothing on the subject, but how can infinity plus infinity equal a static number? the closest answer I can think of to a static number is 2. 2 infinities... Which isn't exactly static. :bugeye:Zeno's paradox relies on the assumption that the sum of an infinite number of numbers must always be infinite, which is incorrect
So how long does it take for a cesium atom to vibrate, and why can't that amount of time be cut in half a-la-Zeno's Paradox?And yes, there is a set unit to measure time by; we currently use vibrations of cesium atoms, which are quantifiable whole numbers.
The sum of an infinitely long set of numbers can be equal to a discrete number if the numbers being added together decrease with each addition. For example, the sum of 1 + ½ + 1/4 + 1/8…taken to infinity will equal two. This is the same thing that happens with zeno's paradox. You have to sum an infinite number of time-lengths to calculate the total time necessary to travel the distance, but the result is not infinite; it's a discrete number. They didn't have the concept of calculus limits back in zeno's time, so he can be forgiven for being mistaken, but it's no longer a paradox.Originally posted by notme2000
Ok, I know next to nothing on the subject, but how can infinity plus infinity equal a static number?
It takes exactly 1/9,192,631,770 seconds for a cesium atom to vibrate; this is the definition of second.So how long does it take for a cesium atom to vibrate
No. The limit of an infinite sum is not an approximation; it is an actual value. The summation of 1+1/2+1/4...will actually be 2 if extended to infinity. Note that it will only actually be 2 (rather than simply very close to 2) if the sum is extended to infinity. It's true that if you extended the sum to a discrete but very large amount that it would not actually equal 2, but at infinity the difference between 2 and the value of the summation will be 1/infinity, which is zero.What we are saying here is that once the numbers get too small, they are not important anymore (what is pretty wrong to think, actually).
I agree qith that but there will still be infinite numbers between 1 and 2. Besides, the highlighted part is what you should pay more attention, which is THE evidence of Zeno's paradox. There are infinite numbers between all natural numbers. Actually, there are infinite numbers between all numbers. That is the focus of Zeno's paradox. See again the series:No. The limit of an infinite sum is not an approximation; it is an actual value. The summation of 1+1/2+1/4...will actually be 2 if extended to infinity. Note that it will only actually be 2 (rather than simply very close to 2) if the sum is extended to infinity. It's true that if you extended the sum to a discrete but very large amount that it would not actually equal 2, but at infinity the difference between 2 and the value of the summation will be 1/infinity, which is zero.
1)If we have an infinite geometric sequence which first term is 4 and ratio is 1/2 then... series:
4+2+1+1/2+1/4+1/8+1/16....
Theorically, the sum is 8.