# SICP Exercise 2.09

Let's use different representation for intervals, namely \((x,\Delta x)\), \(\Delta x\geq 0\), which corresponds to interval that spans from \(x-\Delta x\) to \(x+\Delta x\). Note that we can multiply intervals by real numbers, e.g. \(c(x, \Delta x)=(cx,|c|\Delta x)\). When \(x>0\), \(y>0\), \(\Delta x\ll x\) and \(\Delta y\ll y\), we have the following formulae: \((x,\Delta x)+(y,\Delta y)=(x+y,\Delta x+\Delta y)\) \((x,\Delta x)-(y,\Delta y)=(x-y,\Delta x+\Delta y)\) \((x,\Delta x)\cdot(y,\Delta y)=(xy,x\Delta y+y\Delta x)\) \((x,\Delta x)/(y,\Delta y)=(xy,x\Delta y+y\Delta x)/y^2\). So, for multiplication and division the width of the resulting interval depends on \(x\) and \(y\), not only on \(\Delta x\), \(\Delta y\).