A Debate on Time

Pro has conceded that my point a (infinity can be written as an addition of finite values.) is correct. However, it fails to apply to time, which pro describes with the following series (a+x=b,b+x=c,c+x=d...). Proof that the above series can equal infinity. 1.a+x=b 2.b+x=c 3.(a+x)+x=c | substitution, 1 and 2 4.c+x=d 5. ((a+x)+x)+x=c | substitution, 3 and 4 6. let f(n)=nth variable in sequence (f(1)=a,f(2)=b)) 7. we can see that f(y)=f(y-1)+x, where f(0)=a 8. f(n)=a+(x+x+x...+x) 9. f(n)=a+nx | looking back at our definition, at f(0) there is 0 n, then 1 n is added every time 10.nx can be infinity | pro has conceded this by granting my point A 11. f(n) =a +nx = a + infinity=infinity; when n=infinity 12. (a+x=b,b+x=c,c+x=d...) contains every f(n) where n is a positive integer | definition of f(n) 13. (a+x=b,b+x=c,c+x=d...) contains infinity Pro does provide a direct argument as to why his series must be finite, and while the more mathematically minded users will see a clear response to that in my proof, i will provide a direct response. 1. pro defines a as the start (lets say 0), and x as the increment (lets say 1) 2. let f(n)=the nth term in the series 3. f(1)=a+x | given by pro 4. f(n)=f(n-1)+x | pro was replacing a with the previous term in the sequence, so (a in f(n))=f(n-1) 5. assume x>0 6. f(n) will be greater than 0, at some point in the series 7. y is defined as f(y)=0 8. let f(n)=f(y+z) 9. f(y+z)=f(y)+zx | in f(n) every increase in n is matched by an increase in x, of the same amount as the increase in n, in the expanded form 10. f(y+z)=0+zx=zx 11. pro has conceded that zx can be infinite. | (it is no different than nx, but i was already using n elsewhere in the proof) 12. f(y+z) can be infinite | 10,11 13. f(n) can be infinite | 12,8 Pro is correct in saying my B is not a proper proof, i intended it to be a counter to the unspoken proof by contradiction underlying your arguments, and existing in the heads of most of the readers. C) Sorry, you did clearly specify that i did not have to disprove your side, so let me modify my argument as a proof for my own -1. x is infinite xor x is finite | a xor b means that a or be is true, but not both 0. Assume time is finite 1. All finite series have a beginning and an end 2. let x=the age of time at it's end 3. one second later, the age of time is x+1 4. we have a contradiction (2,3) 5. therefore our premise that time is finite is false 6. therefore time in not finite 7. time is infinite xor time is finite (-1) 8. time is infinite xor FALSE (6,7) 9. a xor FALSE, means a must be true 10. time is infinite is true (8,9) 11 time is infinite Now that i used up some extra space, i can deal with the rest of pros concerns 1. By definition a finite series has a beginning and an end. 2. Therefore, if time is finite it has an end. 3. We are not yet at the end of time, because we still have tomorrow. 4. At the end of time, time will have an age x 5. One second later time's age will be x+1 6. x+1>x 7. therefore x is not the age of time at time's end 8. Therefore our assumption that time is finite was false 9. We know that time is either finite xor infinite 10. We know that time is not finite (8) 11. therefore time is infinite (10, 9) In his last point, pro has made my arguement for me, by stating that all real numbers our an unlimited set. 1. We have both shown that time will have an age of all real numbers 2. There our an infinite amount of real numbers 3. therefore time has an infinite amount of ages 4. each age of time takes a amount of time>0 to pass 5. Therefore the total age of time is infinity * (some real number>0) 6. infinity * (some real number>0)=infinity 7 therefor time is infinite