'Daunting Notation' in my experience stops being daunting as soon as people stop trying to memorize and absorb the notation and instead stop and ask 'why do they use this notation?', which is often where knowing the history of the field, especially that specific problem, tends to help - along with a vague knowledge of latin and greek usually. You're almost always, when learning a new math or physics tool, better off looking up the original problem it was meant to solve and trying to work it out yourself for a bit, until even though you haven't solved it you have a strong familiarity with what actually is the problem, then you look at the solution and suddenly the notation makes obvious sense. Take a previous modular arithmetic example. the whole 'modular' and 'modulus' bit in there is just using 'module' in the sense of individual piece with its own distinct importance. That modulus is all that really matters, it's distinct and relevant existence to the problem at hand is why you are even using the method. The notation is just an easier and clear way of writing it in general form. 14 = 2 (mod 12) is simply how you'd write in math notation 'The fourteenth hour of the day looks the same on a clock as the second hour, or the 26th or 38th or 50th.' Of course it would be kind of case specific to just write 14=2 (clock) or 17=10=3 (week) or 367=2 (year) all of which everyone would recognize instantly but would instead be written as 14=2 (Mod 12), 17=3 (Mod 7), and 367=2 (Mod 365)... most notation is like that, just common sense terminology agreed on to be easier to read, not confusable in context with something else, and general enough to be usable for non obvious examples.




That 'no leading zeroes' thing is sort of rubbish though. The reason nothing else has a cyclic behavior without a leading zero is because in base 10 it is impossible to divide 1 by any number bigger than 10 without getting 0.0XXXX, you can't get less than .1 without having a zero, and you obviously can't get a number bigger than .1 when your divisor is greater than 10. Plenty of numbers cycle, 1/81 cycles, it's just that 81 is bigger than 10 so in base 10 it has to have a zero following the radix point. (Decimal point is just the name for the base 10 radix point), so it's absurd to even say that out of an infinite series of integers none else cycle without a zero because only the 0-9 in decimal can produce a number whose reciprocal is greater than .1, it's unique value in that respect is purely an artifact of base 10