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Comment by eloff | Hacker News Reader

Technically as long as the exponent is greater than one it's still exponential growth. But the rest of what you say is on target.

Edit: I'm laughing about the state of maths education in the US after getting downvoted!

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The jokes on me! What I mean to say is that Moore's law is transistors = 2^(t/2). That is it doubles every two years. But if that slows to 10% every two years, it's still exponential. Transistors = 1.1^(t/2). As long as the BASE is greater than one. I shouldn't have said exponent.

The very meaning of an exponential function is that any point t plus a fixed delta t the value is higher than the value at t by a constant factor. If that factor is getting lower over time it is not exponential anymore, even when it stays above 1. Otherwise you could argue that a quadratic function is exponential as well.

This is not the meaning of an exponential function but merely a property of exponential function with a base > 1.

Tell me another function for which this property holds, but that isn't exponential.

Polynomial as you stated.

No, a polynomial does not have a constant factor for every t.

I may have misunderstood your assertion then. Did you mean the following?

Did you mean something like, here exists some delta and t as for every x>y, with y an element of R, f(x+t) > f(x)+delta

You can choose any delta, so that f(t)*constant=f(t+delta) for every t.

I have misunderstood your original comment. You are indeed correct.

Edit: I just noticed that the function which maps x to 0 satisfies this condition as well, but isn't the exponential function if we consider 0 as part of the domain definition. It doesn't matter much for our discussion though.

Actually the growth is on the exponent. The exponent isn't a constant.

Perhaps you should consider the state of "maths" education wherever you're from, since you seem to be fundamentally confusing exponential and polynomial here.

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