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?


  • 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
  • @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-ZXX
    Jan 15, 2018 at 22:56

1 Answer 1


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)

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