Its not the first time I witnessed it, but today another warden made a math trivia and choose the wrong winner because he failed his own math. So I thought maybe some of you need a little help in the order of operations. The trivia today was "1+1*0" to which the answer is "1", but the warden assumed it to be zero. What the warden did was the following: 1+1*0 -> ((1+1)*0) [chained left to right] -> 2*0 = 0 The correct way is this: 1+1*0 -> 1+(1*0) [multiplication/division goes before addition/subtraction] -> 1+0 = 1 This is because of the rule that certain operations are resolved before the others, in this case you do the multiplication before you do the addition. Parentheses go even before multiplication, so if the warden would write "(1+1)*0" then the answer would have been 0. For more detailed information, this article might be helpful: https://en.wikipedia.org/wiki/Order_of_operations
prove that uuhhhhhhhhhhhh Let f be a continuous function from R to R, prove by example that the preimage of a connected set is not necessarily connected.
Every function f with two points a < b which yield the same value should do it, if f isn't constant on [a,b]. For example: x^2, -1, 1, f-1({1})={-1, -1} which isn't connected. sinx, -pi, pi Basically every non constant non strictly monotonic continuous function should work.
yeah it was an exam question and the second part was to add a hypothesis to make it true, all you need is one-to-one
I want to make it clear that if you do this trivia: 1 + 1 * 0 the answer is not 0, order of operations literally always applies and you can't just say it doesn't. Trivias are supposed to be fair and that shit isn't when you give the prize to the wrong answer.