In Section 3.1 of the IOTA Whitepaper it refers to small delta (δ) but does not actually define what it does. Can you help define δ and explain what the equation is trying to tell me?
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A general technique when proving or deducing limits or differentials is to derive what happens if you add a small value (delta > 0, often you also use epsilon if not used in the proof so far) to a large one (t). That is also where the maths joke "let epsilon be less than zero" comes from. I don't know what the exact part of the whitepaper tries to prove since usually when some limits or derivatives are involved I first try to skip over it and try if I can understand the rest without it.– mihi ♦Jan 15, 2018 at 20:48
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@mihi I agree delta is small, but I think t doesn't have to be big necessarily. Similar to when you look at f'(t) ≈ ( f(t+delta) - f(t) ) / delta, where t just has to be in the domain of f.– Phil-ZXXJan 15, 2018 at 22:56
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1 Answer
H(t) represent the expected cumulative weight at time t.
∂ is a way to note a very small delta time.
The first equation explicit the value the H function relatively to the value of the H function a very small time before.
The second equation is the differential of the first one. In other words, dH(t)/dt is the slope of the function H(t)
