This Question Got Me Thinking.

[Marshwarble]

My Dad is thirty years older than me. After an infinite amount of time will he still be older than me?

My initial thought is that there's something self-defeating in the phrase "infinite amount of time" but if anyone can help? Obviously we'd both be dead, so it makes no difference.

[jim360]

I suppose if you were living forever, then yes. Sort of. Although the behaviour at infinity is weird, and you need to be careful about what you are asking in order to ensure you get a sensible answer.

Here, the difference between your ages is going to be 30 years (assuming immortality) for ever; thus, as your ages tend towards infinity the limit of the difference of yours ages would still be 30 years apart. When you're both infinitely old, however, you can't actually make the comparison as you can't add things to infinity.

So the answer is "sort of but not really". I don't know if that's very helpful.

[ToraToraTora]

there was a Jim Al-Khalili maths program on a while ago that dealt with infinity. Apparently there are different sizes of Infinity. For example there are an infinite number of real numbers between 1 and 2 and also between 0.1 and 0.2 so it follows that the numbers between 1 and 2 are a superset of those between 0.1 and 0.2 and thus are a bigger infinity! I can't explain it any further!

[jomifl]

If an object can be divided into an infinite number of parts then does that mean another object can't?

[Mosaic]

My mum was 40 years older than me. She became older and older by choice. So maybe part of the age thing is in the perception. Older is as older does.

[bibblebub]

special relativity suggests that if he were to travel faster than you for a sufficiently long time then you'll catch him up

[Peter Pedant]

Jim if he comes back - would be able to explain the different sizes of infinity as Khal;;i pointed out

thre are an infinite number of fractions 1/2. 1/3. 2/3 1/4. 2/4 and so on
and the points between 0 and 1

but they cant be put into a 1:1 corrspondence which means that they are different sizes ....

Cantor was the first to realise this - and the idea forms the basis of his diagonal theorem
https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

Marshwarble two sets are clearly both countable tho

\lots of understandable books about Infinity
not quite an infinity of the them -
John D Barrow wrote one ( yeah - " Infinity " )
His real claim to fame is that his predecessor and linear ascendent really did say in 1665, "I shouldnt be Lucasian Prof of math - Mr Newton should !" and that sort of thing doesnt happen very often even when you DO identify someone much brighter than oneself ! !

[Old_Geezer]

He is only older than you whilst you are both alive as your ages are measured from the point you were born. It is meaningless outside of life. Consider the situation from the viewpoint of someone who doesn't believe life is all there is for each individual. Given that could there not be an entity that was you before birth ? And your father also ? Then in this larger framework in what way does your father claim to be older than you if you've both been 'around' always ? The question is only valid when both of you are living.

[Marshwarble]

I think you still need to know that one dead person was older than other dead person though. William the Conqueror was older than William Rufus for instance.

[jim360]

I don't think we should overcomplicate things eg by introducing Relativistic effects. Age can be defined, anyway, in an invariant sense as the "proper time" that has passed since birth in a person's own reference frame. With respect to past lives, too, that seems like a distraction. It's enough that whatever you were before, at some point you started to be considered as an entity in your own right.

So with that in mind the only question is whether age still makes sense after death. I think you can do, by saying that a person's age at any given time is how long has passed since their birth, so that, say, Shakespeare would have been 455 years old right now.

With that out of the way, the age difference "at infinity" of two people born 30 years apart is given by D = (x+30) - x, where x is the younger person's age. Given that x - x = 0 (this is cutting-edge maths right here), that tells us that as x gets arbitrarily large, but still has a value, then the age difference is always 30. Best expressed as "the limit of the age difference as the younger person's age tends to infinity is 30". You can't actually ask the question at infinity, because it's not really a number, so this is as good as you can do.

[Old_Geezer]

Was, not is.

[Peter Pedant]

I can still recommend the books on Infinity esp Barrow

cheap on Amaxon and Christmas is coming ....