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Also, a rope that is infinitely long has no tension in it, which means the knot will stay precisely as it is, indefinitely
. It does look like starring down the barrel of a gun though. Don't shoot the crows.
originally posted by: TomServo
Apply the bread slicing comcept to falling. If an object falls off a building, over a period of time, it will fall half way. Then it will fall half way again, and again, and again... So to test the concept, you could jump off a building, and tell me if you ever reach the bottom.
I jest... The point is.. all numbers are actually meaningless without a reference. 0 is typically that reference we assign to the beginning. consider the object you throw off the building. It begins from a realative height. But height from what? in the case of the bread, eventually you will be halving atoms, muons, quarks, etc... I'd rather jump off a building in that case. So I guess in short, dangerous things happen when you approach 0...
originally posted by: IrnBruFiend
If you take any number, and keep halving the value, you will never get to zero. This problem in mathematics is most famously known as the Zeno's paradox. Here's an analogy: Take a piece of bread, with a length of 1. Slice it in half and you have 0.5. Slice it in half again and you have 0.25. Slice it in half again and you have 0.125, etc, etc. You will find the number continues on infinitely when halved and will never reach zero. Theoretically, if you keep slicing the piece of bread in half you will never ever cut the whole thing.
Everything in the physical universe must be made out of at least 1 if something. Yes / no?
This concept draws parallels with infinity. You can take any number and double it to an infinite degree.
Also, you can take any number and half it to an infinite degree. You can never begin with zero; and you can never reach zero. Another example of this can be found in fractals. Below is a visual demonstration of a fractal known as the Cantor set.
What is the smallest thing in the physical universe? Can it be halved? Can it be halved again? If we know what the smallest thing in the universe is, and know it can't be halved for definite, that's fine. Problem solved.
Or is it? What are the implications for the subject of mathematics which is (at least what I consider) the purest of all subjects.
Math is always correct. Isn't it?
If we conclude a particular constitute of a particular can't be halved in the physical universe, does this imply math, being the pure subject that it is,
doesn't accurately correlate with the physical universe?
What if the smallest constitute of the universe can be halved infinitely? Does this imply infinity is a reality and that mathematics is always pure in our understanding of the universe?
Moreover, I have wondered about the Big Bang theory in relation to this.
Can zero exist and not exist?