Can You Be Half Someone's Age More Than Once?

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SUMMARY

It is impossible to be half someone's age more than once due to the fixed age difference between individuals. In the example provided, if a person is born at age 0 while their father is 20, the father will only be twice the age of the child when the child reaches 20. After this point, the age ratio will continue to decrease as both ages increase linearly over time. The discussion emphasizes the mathematical principle that the age difference remains constant, leading to a diminishing fraction of age comparison.

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KingBigness
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Homework Statement


I need a rock solid proof.

Is it possible to be half someones age more than once?

Eg. I was born at 0 while my dad was born at 20, he will be 40 when I am 20 hence I am half his age. Is this possible more than once?
 
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The difference in your ages is fixed. Use that constant to show that the fraction only ever decreases.

(Quibble: in your example, if I die when I'm 30, will I again be half my Dad's age when he turns 60?)
 
You have two ages, which can be represented by functions which are linear in time, what do you know about the solutions to systems of linear equations?
 

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