Small steps

If you get a little better every day, the days add up. One per cent better each day is not much on its own.

A little better every day adds up. $1\%$ a day is small on its own.

$\forall$ day: better by $1\%$. One day: $\times 1.01$, small.

But after a year, one per cent a day, compounded, makes you about thirty-eight times better than you started. One per cent worse each day leaves almost nothing.

After a year: $(1.01{)}^{365}\approx 37.8$, about $38$ times better. And $(0.99{)}^{365}\approx 0.03$: almost nothing left.

$(1.01{)}^{365}\approx 37.8$. $(0.99{)}^{365}\approx 0.03$.

So the rule is simple: every day, one small step. Not a big one, and never none.

The rule: $\forall$ day, one small step. $>0$, never $=0$.

rule: $\forall$ day, step $>0$. $\nexists$ day with step $=0$.

Big goals are only sums of small days. Nobody climbs a mountain in one step; everybody climbs it one step at a time.

A big goal $=\sum$ small days. No one climbs in $1$ step; everyone climbs in $n$ steps, $n$ large.

goal $={\sum }_{i=1}^n{s}_i$ ($s_i$ = the step of day $i$). mountain: $n\gg 1$.