Infinity: Philosophical Considerations

Originally posted by josephw
Infinite blah blah blahs.

[b]Infinite. The opposite of finite. Finite=numerable. Infinite=innumerable.

Sometimes I think you guys just like to think something is more complicated than it really is.

Maybe somethings are just too simple for you to understand. idk[/b]

Thank you, as often, we're on the same page, page number infinity. 🙂

Originally posted by sonhouse
Wouldn't that just be 1/5, inverse of 5? 1/infinity?

Inverse is not the same as opposite. Thus, infinitesimal wouldn't be the opposite of infinite.

Originally posted by tomtom232
Inverse is not the same as opposite. Thus, infinitesimal wouldn't be the opposite of infinite.

So whose right ? You or sonhouse?

Originally posted by karoly aczel
So whose right ? You or sonhouse?

The "opposite" of a number simply means you put a negative sign in front of it, or take the negative sign away if it's already negative.

The "reciprocal" or "multiplicitave inverse" of any number x is 1/x or x^-1.

So for the number 5...the reciprocal or multiplicative inverse of 5 is 1/5, the opposite of 1/5 is -1/5.

If you do it the other way around, the opposite of 5 is -5, and the reciprocal/multiplicative inverse of -5 is 1/-5 = -1/5, so either way you get the same answer.

What sonhouse gave was the multiplicative inverse or reciprocal.

Edit: a+(-a) = 0 -- for any number a there exists a unique opposite number (-a)

Edit: Also, infinity isn't a number so 1/infinity is undefined but I take it to mean "infinitesimal."

Originally posted by tomtom232
The "opposite" of a number simply means you put a negative sign in front of it, or take the negative sign away if it's already negative.

The "reciprocal" or "multiplicitave inverse" of any number x is 1/x or x^-1.

So for the number 5...the reciprocal or multiplicative inverse of 5 is 1/5, the opposite of 1/5 is -1/5.

If you do ...[text shortened]... inity isn't a number so 1/infinity is undefined but I take it to mean "infinitesimal."

So is "infinity/eternity" like a "door" where mathematics takes you up to, but only metaphysics can take you beyond?

Can you work with that analogy and if not , why not?

Originally posted by karoly aczel
So is "infinity/eternity" like a "door" where mathematics takes you up to, but only metaphysics can take you beyond?

Can you work with that analogy and if not , why not?

No, I can't work with that analogy because there is no "beyond" to infinity. Not even god is "beyond" infinite.

Mathematics doesn't take you there it is just the mathematical concept for any number x there is a number x+1 (I am unaware of a way to show uncountable infinity without using aleph numbers).
There are many uncountable sets(infinite sets) but the most known is the set of real numbers (an uncountable set is one with a cardinal number[there is a transfinite sequence of cardinal numbers] larger than that of the set of all natural numbers.)

The set of all natural numbers is N={1,2,3,...} and the set of real numbers is R={x: x is a real number}. The cardinality of R is 2^Aleph-0 or Beth-1 and is called the cardinality of the continuum.

However, infinity is a valid metaphysical topic but I think it has already been clearly defined earlier in this thread.