brightsky's Noob-tastic Question Thread

[iNerd]

Can someone clarify, does R^+ / R^- include 0 or not? I remember reading something about this on VN but I can't find it. :/

From my knowledge it's neither. Don't go on me though -.-

[luken93]

R+ = (0, infinity)
R- = (-infinity, 0)
R+ u R- = R\{0}
R = (-infinity,0) u {0} u (0, infinity)
Source: wolfram

[iNerd]

R+ = (0, infinity)
R- = (-infinity, 0)
R+ u R- = R\{0}
R = (-infinity,0) u {0} u (0, infinity)
Source: wolfram

I'm confused? Doesn't circle bracket mean not included? So was I right? R+ or R-, neither includes 0?

[luken93]

R+ = (0, infinity)
R- = (-infinity, 0)
R+ u R- = R\{0}
R = (-infinity,0) u {0} u (0, infinity)
Source: wolfram

I'm confused? Doesn't circle bracket mean not included? So was I right? R+ or R-, neither includes 0?

correct

[burbs]

yes.

R does not specifically have 0 which is why luken has done U{0}

if a graph has a domain of like [0,infinity) you could say R+ U{0}

[m@tty]

It depends, sometimes is taken as non-negative real numbers, while at other times it means positives only.

I would say when answering questions take it as the positive reals and if needed go just to be unambiguous.

[TrueTears]

yes.

R does not specifically have 0 which is why luken has done U{0}

if a graph has a domain of like [0,infinity) you could say R+ U{0}

is defined to contain 0.

http://en.wikipedia.org/wiki/Real_number

[brightsky]

Just another question, how does one reflect any graph about a certain line ax + by + c = 0?
So for instance, if I wanted to reflect the curve y = sqrt(x) about the line y = 1/2 x + 5, what would the equation of the resulting graph be?
Thanks.

[xZero]

We did something similar in my maths unit, basically you rotate the line y = 1/2 x + 5 so it's parallel to the x-axis, do the same rotation with the line ax + by + c = 0, reflect it by the rotated line which is parallel to the x-axis (easy) then rotate it back. Not sure if theres a easier method

[moekamo]

when rotating(CCW) about another line that makes an angle of with the positive x axis, you apply the matrix transformation:


you would then solve for x, y or eliminate the somehow and put them into the equation y=sqrt(x) and simplify, which im not sure if it can be done or not... maybe someone else with awesome skills can tell you if its possible...

[enpassant]

Just another question, how does one reflect any graph about a certain line ax + by + c = 0?
So for instance, if I wanted to reflect the curve y = sqrt(x) about the line y = 1/2 x + 5, what would the equation of the resulting graph be?
Thanks.

Using high school maths
find the intersection of the two lines and the angle between them
the reflection is a line through the intersection and make the same angle on the other side

[brightsky]

Just another question, how does one reflect any graph about a certain line ax + by + c = 0?
So for instance, if I wanted to reflect the curve y = sqrt(x) about the line y = 1/2 x + 5, what would the equation of the resulting graph be?
Thanks.

Using high school maths
find the intersection of the two lines and the angle between them
the reflection is a line through the intersection and make the same angle on the other side

Which two lines are you referring to?

when rotating(CCW) about another line that makes an angle of with the positive x axis, you apply the matrix transformation:


you would then solve for x, y or eliminate the somehow and put them into the equation y=sqrt(x) and simplify, which im not sure if it can be done or not... maybe someone else with awesome skills can tell you if its possible...

I saw this matrix on Wikipedia, but I'm not sure how it is derived. And where does the given linear equation about which you reflect it come into play?

We did something similar in my maths unit, basically you rotate the line y = 1/2 x + 5 so it's parallel to the x-axis, do the same rotation with the line ax + by + c = 0, reflect it by the rotated line which is parallel to the x-axis (easy) then rotate it back. Not sure if theres a easier method

Hmm, never thought of that...seems like a good way.

[brightsky]

In the notation , what does the second R mean?
Also with the transformation , what do the first and second R^2s mean respectively?

[luken93]

The second R is known as the co-domain, and it specifies the field of y-values that f(x) allows. It's different to the range, because the range is the corresponding values of f(x), whereas R is more of a restriction of values... Oh, and for methods it'll always be R

Can't remember what the R^2 means though XD

EDIT: Read this for R²

[brightsky]

The second R is known as the co-domain, and it specifies the field of y-values that f(x) allows. It's different to the range, because the range is the corresponding values of f(x), whereas R is more of a restriction of values... Oh, and for methods it'll always be R

Can't remember what the R^2 means though XD

ahh makes sense, thanks luken!