You agree it is not temporal but then go on to say that this output depends on the function's previous output, and so on so forth. Temporal matters are those of change, change is time. If you are talking about function outputs as if they are changing with each iteration then you are talking about time. As our temporal minds analyze the function we perceive it as if it were changing, but it is not. As soon as that function is called into existence it at that same moment already and forever equals its final output.

It's not that the one number "changes" as the others change, as if in time. It's that the one number is logically contingent upon the other numbers.

Suppose I said that I am thinking of a number

*a*, whose value is defined as being equal to that of some other number

*b*, plus one. And the value of

*b* is defined as being equal

*c* + 1. And so forth, ad infinitum. And then I ask myself, what is the value of

*a*? The answer is, it has no value. Because it only has value insofar as

*b* has value, and

*b* only has value insofar as

*c* has value. Each number is relative to something else, so without that absolute starting point then nothing else has any value. And if the chain goes on forever (which it does, since it's an

*infinite* series) then there is no starting point. Thus, if I know in advance that

*a* has a value, then I also know in advance that the chain must terminate at some starting point (and that the series must be finite). No starting point means no value.

Now suppose it was not an infinite chain but it was just three numbers:

*a*,

*b*, and

*c*. If

*c* was defined as 10, then

*a* would be 12, by definition. Not because of the passage of time (as if, in a temporal succession,

*b* first becomes 11 in response to

*c*'s value, and afterwards

*a* becomes 12 in response to

*b*'s value). Rather,

*a* would simply be 12 by the very fact that

*b* is 11, by the very fact that

*c* is 10.

There is no time in math for it is supernatural. The infinite series simply is equal to what it is equal to. There is no + 9 and then + another 9 and another 9 forever. It simply is 1.

Remember, the value of a series is not the result of an algorithm or a procedure that can be completed, it is by definition the limit of the nth partial sum of the series as n increases without bound. You do not have to assume you can actually add an infinite number of terms as you would add a finite number of terms. You clearly cannot do that.

To clarify, it seems that both of you are saying that a summation is not the same thing as repeated addition? (Or, at least not

*always* the same thing?)