# How to check if $x$ equals a certain value $y$ with while loops, addition and substraction

Consider, we are only allowed to use loops ($$while$$), addition ($$+$$), substraction ($$-$$) and checking if a value is $$> 0$$. How can one find out, if a certain variable $$x$$ equals a value $$y$$? E.g. how can I find out if $$x=4$$ by only using the aforementioned methods? For $$x=0$$ I came up with the following:

y = 1
while x > 0:
y = y - 1
x = x - 1
while y > 0:
do something


This way, $$something$$ gets only executed if $$x=0$$. But I have no clue about values above $$0$$.

Start by calculating $$x-y$$. This is simple enough:
while y > 0:

Now, compare what you got with $$0$$. That is, compare the value of $$x$$ after the loop to $$0$$, using the technique you thought of. This will guarantee that "$$something$$" is executed only if $$x-y=0$$, or equivalently if $$x=y$$.