Ytukyg

up vote 0 down vote favorite My question is NOT “why does the product topology satisfy the conditions of a categorical product in Top ”. Rather, my question is, why does it do so uniquely? I don’t require necessarily a fully rigorous proof, but an conceptual understanding. My guess is: If we take the cartesian product between two topological spaces $X,Y$ , but we endow this product with a trivial topology ${emptyset, Xtimes Y}$ , then this also satisfies the categorical product conditions: For any topological space $Z$ and continuous functions $f:Zto X, g:Zto Y$ , there is a unique function $h=ftimes g:Zto Xtimes Y$ . We don’t need to put any more conditions on the topology of $Xtimes Y$ for $h$ to be unique. (This is essentially because the cartesian product $Xtimes Y$ is already “set-theoretically restricted” enough to e

up vote 1 down vote favorite In Ruby, I get: -5 % 3 # => 1 whereas other languages like PHP, Javascript, C++, and Java all produce the result -2 . I don't understand this concept. I hope someone can explain this ruby's calculation method. It would be better if you could use an example of how it works. ruby share | improve this question edited Nov 21 at 5:50 sawa 128k 27 193 297 asked Nov 19 at 16:06 Pradhumn Sharma 111 6