I have 2 questions I need help with.
(1) Solve the following equation for x (in the real numbers):
x^2 - 2x + 3 = 0.
(2) Let X be a topological space. Show that if X is second countable, X is Lindelof.
For (1), I have no idea how to do this one.
For (2), here's my idea. Let B be the countable basis of X. Let S be the set created as follows. For each b in B, take some x in b and put it in S. Clearly, S is countable. I claim S is also dense, and therefore X is Lindelof. So I will show X is a subset of the closure(S) = S union (LimitPointSet(S)). Take y in X. If y is in S then y is in closure(S). If y is NOT in s, show y is in LimitPoitnSet(S). Does this make sense?
Thanks guys!
(1) Solve the following equation for x (in the real numbers):
x^2 - 2x + 3 = 0.
(2) Let X be a topological space. Show that if X is second countable, X is Lindelof.
For (1), I have no idea how to do this one.
For (2), here's my idea. Let B be the countable basis of X. Let S be the set created as follows. For each b in B, take some x in b and put it in S. Clearly, S is countable. I claim S is also dense, and therefore X is Lindelof. So I will show X is a subset of the closure(S) = S union (LimitPointSet(S)). Take y in X. If y is in S then y is in closure(S). If y is NOT in s, show y is in LimitPoitnSet(S). Does this make sense?
Thanks guys!
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You're stupid and should quit maths. Did I win at worst answer?
1. The discriminant is (-2)^2 - 4*3 = 4 - 12 < 0 so there are no real solutions.
2. By definition X has a countable basis. Let C be an open cover of X, then every set in C is the union of a subset of the basis B. Hence C is the union of a subset of B. The union of a subset of B is then a countable subcover of C so X is Lindelof by definition
1. The discriminant is (-2)^2 - 4*3 = 4 - 12 < 0 so there are no real solutions.
2. By definition X has a countable basis. Let C be an open cover of X, then every set in C is the union of a subset of the basis B. Hence C is the union of a subset of B. The union of a subset of B is then a countable subcover of C so X is Lindelof by definition
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Look at all of the atheist history scholars with their "Hitler was a Christian" chants. Sadly, the facts do not agree with these atheists.
Hitler on Christianity, as recorded by his personal secretary and published in the book "Hitler's Secret Conversations."
"Christianity is a rebellion against natural law, a protest against nature. Taken to its logical extreme, Christianity would mean the systematic cultivation of the human failure." -- 10th October, 1941
"Christianity is an invention of sick brains: one could imagine nothing more senseless, nor any more indecent way of turning the idea of the Godhead into a mockery.... .... When all is said, we have no reason to wish that the Italians and Spaniards should free themselves from the drug of Christianity. Let's be the only people who are immunised against the disease." -- 13 December, 1941
"There is something very unhealthy about Christianity." -- 9 April, 1942
Sure sounds like Hitler was a model Christian, doesn't it?
Hitler on Christianity, as recorded by his personal secretary and published in the book "Hitler's Secret Conversations."
"Christianity is a rebellion against natural law, a protest against nature. Taken to its logical extreme, Christianity would mean the systematic cultivation of the human failure." -- 10th October, 1941
"Christianity is an invention of sick brains: one could imagine nothing more senseless, nor any more indecent way of turning the idea of the Godhead into a mockery.... .... When all is said, we have no reason to wish that the Italians and Spaniards should free themselves from the drug of Christianity. Let's be the only people who are immunised against the disease." -- 13 December, 1941
"There is something very unhealthy about Christianity." -- 9 April, 1942
Sure sounds like Hitler was a model Christian, doesn't it?
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x^2 - 2x + 3 = 0.
x=9 x= 10
Am I worst??
If Yes 10 Points
x=9 x= 10
Am I worst??
If Yes 10 Points