or else destroy most all physics and mathematics. Infinity and zero do not go hand in hand.
The problem is in the definition of division.
Multiplication is the sum of many equal terms by definition. Division is then the number of terms given the value of the sum and the term.
If the value of the term is zero, we know that the sum is zero no matter how many terms you add up. Multiplication is defined for absolute zero.
Division is undefined because it asks an impossible question. How many zeroes do you have to add up before you get a non-zero answer. There is no answer to that question. If you keep adding zeroes your sum remains zero. Infinity is just a language construct to say that there is no answer.
So actually if you can define an absolute zero, then you cannot define an absolute infinity. The two concepts are out-of-hand.
But like in LQG, you cannot define an absolute zero. There is always a little tiny something- no such thing as a vanishing point. Nothing is continuous.
So if we make the term have the value of that minimum number, then we can never define a sum to be zero. Zero cannot exist.
Infinity in some sense can exist, for as you take more and more terms into your sum, the summ gets larger and larger until we can rightfully call it infinite because the properties of that sum do not change as we add more terms. In some cases just a million terms will do.
So if absolute zero does not exist, then an operational infinity can exist, and vice versa. If zero can exist, then infinity cannot exit, except in the nonsense limit that adding up zeroes, sums to zero, even for one,or two, or three terms. So the nonsense is that using the definition of infinity as the number of terms to yield unchanging properties of a sum; with the existense of absolute zero, the number 2, 0r 3,... are infinite. All numbers but 1 are infinite.
So keep the concept of absolute zero as a convenient approximation to the Planck scale, and forget about infinity. But realize that nothing is absolute zero and using the actual minimum size of anything allows for a realistic operational definition of infinity. |