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Yes! f(x) is y. That is, symbol f(x) is another way of expressing the y variable (called function notation). No, that's my fault. :oops: Post...

The nth index value is n-1 only when the index starts at 0. Were you to start with index 2, instead, you would be starting with a value that is...

For example if I have 2^3 possibilities, why the indexes from 0-(2^3 -1) will label all 2^3 possibilities? I claim that the last label/index must be...

firstly thanks for your cooperation ; secondly but I can also labeling the indexes as 2 is the 1st index 3 is the 2nd index 4 is the 3rd index...

Symbol n tells us how many index numbers we have. (When the index value starts at 1, then the value matches the count. That is, the nth index's value...

\dfrac{12}{35} \Rightarrow \text{Pretty darn close to }\dfrac 1 3 \text{ but still }\Rightarrow \text{corner}

ur explanation straight forward, helped me very much!

thanks ! yup helped me

I'll handle that. :cool:

I thought it was a riddle. ;)

What did you try?

So what we have here is: \forall x (\exists y F_{xy} \implies \forall y F_{yx}) \exists x \exists y F_{xy} \therefore \forall x \forall y...

Before retiring I loved to teach combinatorics at a simple level to in service teachers. They need renewal credits and a collection of problems...

My 1/3 assumes completely at random. Plus 1/3 also solution to all similar cases > 1 couple. Do I get the "corner" again?

I feel like such an idiot right about now...I just realized I posted that image in a staff area at the other site. D'oh!!! I've posted the image...

Sorry for the late reply, so when you say f(11)=75 does that mean I need my y value to equal 75 if I was to plug in a number for x (like in the...

I agree that \cos(x)^2 is at least a little ambiguous, and therefore risky to use, especially with inexperienced readers. In a context where one...

No, I claim it is not consistent function notation for the exponentiation of trig functions to begin with.

Thanks for adding this perspective. I thought some of what he said sounded too restrictive. By the way, isn't your final claim circular, since the...

Assignment with proper questions: https://ibb.co/nBwmcRf My work on grid paper: https://ibb.co/2nc20Tp I graphed the sin function with the proper...

Did you see posts #7, #8 and #9? :-?

I don't understand your statement (followed by question marks). Do you have a value for x?

It's not ambiguous, for folks who understand function notation. Is your position that it shouldn't be used because you think a majority of people do...

but, should it not be m2-3m + 3 and so (m-3/2)2 +3/4 >= 0?

The former is poor form if it is intended to be equivalent for the square of the cosine of x, because it has ambiguous style. It should not be...

It isn't. Some of the replies contain a mistake. At the end of post #4, Dr. Peterson gives you some suggestions on how to show that for all Real...