I was mulling this little thought over in my head today, but I can't seem to prove or disprove it to myself. Can any of you phrase a convincing response? Here Goes:
On a graph, between any two given points, let's say 1 and 2, there is an infinite amount of points.
There is also an infinite amount of points between 1 and 1,000,000.
Infinity=Infinity
Therefore the distance between 1 and 2 is the same as the difference between 1 and 1,000,000, right?
I was mulling this little thought over in my head today, but I can't seem to prove or disprove it to myself. Can any of you phrase a convincing response? Here Goes:
On a graph, between any two given points, let's say 1 and 2, there is an infinite amount of points.
There is also an infinite amount of points between 1 and 1,000,000.
Infinity=Infinity
Therefore the distance between 1 and 2 is the same as the difference between 1 and 1,000,000, right?
yeah well, if Santa was an evil robot who put everyone on the naughty list, even those who are nice, Santa is therefore being naughty. is that really the kind of robot you want your children to look up to? is it?
no. There is a certain amount of points between 1 and 2. We just don't have the number for them. If you're talking about a distance, then it is one number, and it is a set amount.
if the distance between the points is one unit, then as there are infinite points, the point is 1/infinity across. essentially zero. same for 1,000,000/infinity.
you cannot measure between two points by how many points you can fit in between them, because its like saying how many times do you need to +0 to get from 1 to 2?
Hmm yea I understand now. Points aren't distance. There is still a set distance between 0 and 1, but that distance can be subdivided into infinite points. Therefore if you had a line from 0 to 1 and a line from 0 to 2 then they would both contain infinite points but the line from 0 to 2 would contain all of the infinite points of 0 to 1 plus the points that the shorter line does not contain.
This reminds me of thescenariothat if you had an infinite number
ofmonkeys sitting at an infinite number of typewriters for an infinite number of years typing at random
then it could be accepted as a probability that one would eventually type the entire works of Shakespeare!
BTW...the numbers between 1 and 2 are not infinite.
Greenwhitegreen
Yes it is. Try counting from 1 until you reach an end point. Can't be done right? The number keeps getting bigger and bigger. Now imagine the same thing with a decimal. A number can continue to have an infinite number of decimal places because no matter what number a number is, there will always be something bigger or smaller than it.
Even if what you said was true, infinity is a concept, and can't be used with the transitive property anyway. Plus the fact that there are different sizes of infinity, which only complicate things more.
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