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new chars/structures on this page

infinity
a fused number 1 and plus symbol
output is looped back into an input
defined as { while(true){x+=1;} return x;} = infinity

1 / infinity

apair array pairing op
{1 , 2 , 3} apair {a , b , c} = { {1 , a} , {2 , b} , {3 , c} }
we define its behaviour "enough for now".
Enough to use it for basic calculus.

X Y dx dy

x1. first x in an interval x2. second x in an interval

y1. first y in an interval y2. second y in an interval

dx/dy.
change/slope of X (vertical)
from perspective of one Y (horizontal) unit

dy/dx.
change/slope of Y(horizontal)
from perspective of one X (vertical) unit

area with respect to X (under curve)

area with respect to Y

the array interval gap before an element

the array interval gap after an element

the array interval gap between two elements





full page desc content

infinity array pairing _img graph.svg img_ Arbitrary! dont rant at me about why these choices are not universal.. they are NOT universal. right vs left = completely arbitrary up down has a bit of physical and abstract intuition. but you could easily find equally valid intuitions to argue for the opposite. should expand on the definition of 'reverse' gaps, which look at an interval backwards inverting the x1,x2 sequence and thus inverting the sign change the example so that it is offset from origin (like just a +1) so that way the xarea and y area are different in the examples *show* inf :: infinity
a fused number 1 and plus symbol
output is looped back into an input
defined as { while(true){x+=1;} return x;} = infinity divinf :: 1 / infinity apair :: apair array pairing op
{1 .. 2 .. 3} apair {a .. b .. c} = { {1 .. a} .. {2 .. b} .. {3 .. c} }
we define its behaviour "enough for now".
Enough to use it for basic calculus. x :: X , y :: Y ,dx :: dx , dy :: dy x1 :: x1. first x in an interval, x2 :: x2. second x in an interval y1 :: y1. first y in an interval, y2 :: y2. second y in an interval dxdy :: dx/dy.
change/slope of X (vertical)
from perspective of one Y (horizontal) unit dydx :: dy/dx.
change/slope of Y(horizontal)
from perspective of one X (vertical) unit xarea :: area with respect to X (under curve) yarea :: area with respect to Y s[ .. v1] :: the array interval gap before an element s[v1 .. ] :: the array interval gap after an element s[v1 .. v2] :: the array interval gap between two elements