RE: Jesus as Lord - why is this appealing to so many?
February 13, 2018 at 5:39 pm
(This post was last modified: February 13, 2018 at 5:40 pm by polymath257.)
OK, first some definitions.
Finite means it can be counted by some counting number or some 'real' number. Infinite means it is not finite.
So, a line segment of length 1 inch is 'finite' in length, but has an infinite number of points on it, so is infinite in terms of number of components. It is 'bounded', but also infinite. Similarly, anything with finite, non-zero volume will have an infinite number of components.
(This goes to show the definition of infinite in terms of boundedness is not a very good one).
The negative integers {..,-3,-2,-1} are unbounded below and bounded above. This is an infinite set because the number of negative integers cannot be counted by a finite number. That doesn't detract from its being bounded above (by 0). This is an example of a set that is bounded in one sense, but unbounded in another.
So, yes, you can have an actual infinite (like the negative integers) that is also bounded above. Not finishing isn't a criterion: the set is complete in and of itself.
Since I don't believe in any God, I can't say what you think about his/her/its infinite nature.
The water example shows that large collections can appear to be continuous when in fact they are not. So?
Finite means it can be counted by some counting number or some 'real' number. Infinite means it is not finite.
So, a line segment of length 1 inch is 'finite' in length, but has an infinite number of points on it, so is infinite in terms of number of components. It is 'bounded', but also infinite. Similarly, anything with finite, non-zero volume will have an infinite number of components.
(This goes to show the definition of infinite in terms of boundedness is not a very good one).
The negative integers {..,-3,-2,-1} are unbounded below and bounded above. This is an infinite set because the number of negative integers cannot be counted by a finite number. That doesn't detract from its being bounded above (by 0). This is an example of a set that is bounded in one sense, but unbounded in another.
So, yes, you can have an actual infinite (like the negative integers) that is also bounded above. Not finishing isn't a criterion: the set is complete in and of itself.
Since I don't believe in any God, I can't say what you think about his/her/its infinite nature.
The water example shows that large collections can appear to be continuous when in fact they are not. So?
