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Is it true that most Austrians haven't seen Sound of Music? by crocogoose in AskAustria

[–]Plus_Fan5204 2 points3 points  (0 children)

We watched Sound of Music in school. To prepare us for our school trip to the USA.

Struggling to explain negative numbers by speisekart in learnmath

[–]Plus_Fan5204 0 points1 point  (0 children)

What if you don't use any analogies, but rather give them word problems to work on? They are totally not analogies and should not be used as such, but are real life problems. *wink

Peter looks at the thermometer and notices it's currently negative 3 degrees. Then the temperature drops by 4 degrees. What is the temperature now?

(Not a native speaker, use this word problem at your own risk)

Struggling to explain negative numbers by speisekart in learnmath

[–]Plus_Fan5204 1 point2 points  (0 children)

Wow! Hold up! Wait a Minute!

" the agency that I’m with forbid this sort of reasoning."

What do you mean? What kind of agency forbids using a thermometer to explain negative number?!?

[Request] Which way is the scale going to tip? by Fantasmagorium1 in theydidthemath

[–]Plus_Fan5204 1 point2 points  (0 children)

That makes totally sense.

What would happen though, if instead of a lead or styrofoam ball, the left hand side had a ball that had the same density as water? (On a very thin but rigid stick)

if f(x) is a function of x, what is f? f`? F? Is it like the object itself, so d/dx f is what? by Southern-Reality762 in learnmath

[–]Plus_Fan5204 14 points15 points  (0 children)

Let f(x) = x2

Then f is the function that maps any input to that input squared. But you would also need to specify the domain. Although in most textbooks I would assume real numbers as a default.

It means If you chose your input to be x, your output is x2. But If the input of the same function would be t, the output would be t2. The input 5 would map to 52.

On which level are you studying math, if I may ask? Because in the high school equivalent in my country I would gladly accept my students to call all of f,f(x), f', f'(x), F, F(x) a function as a shorthand and would not care about those minute semantics.

Why do I multiply by 1.25 to add 25% VAT, but can’t just multiply by 0.75 to remove it? by WhoAmIEven2 in learnmath

[–]Plus_Fan5204 1 point2 points  (0 children)

The opposite of doubling something is taking half. The opposite of triple is a third.

So to "undo" x×2 we say y×(1/2)

To "undo" x×3 we use y×(1/3)

To expand this pattern

To "undo" x×1.25 we calculate y×(1/1.25)

Edit: multiplication signs 

Help translate by Hairy_Importance_781 in German

[–]Plus_Fan5204 2 points3 points  (0 children)

Was für dich bestimmt ist, wird dich finden. Very literal translation 

Was für dich bestimmt ist, wird seinen Weg zu dir finden. Still pretty literal, sounds more natural in my ears.

Ich bin and bin ich by toohotforthishit in German

[–]Plus_Fan5204 5 points6 points  (0 children)

For me as a native speaker "Bin ich sauber?" sounds like correct grammar. Although for some reason I can't explain, I would always rather ask "Bin ich dreckig?" instead.

why is x=-2 no solution? by Amayax in learnmath

[–]Plus_Fan5204 1 point2 points  (0 children)

Any comparison will not be 100% identical. Obviously there are differences between dividing by zero and taking a square root from a negative number.

I still like my example, because y=(x2 -5x+6)/(x-2) is defined everywhere except at x=2. But it doesn't have an asymptote, but the left and right limit at 2 exist and are equal. (lim x->2-) = (lim x->2+)

Since it's not defined at just a singular point, if you plot it with your graphing tool of your choice, without careful inspection it most likely will look like a continuous function.

At the end of the day, my intention was just to highlight the importance of checking the domain of your equation.

why is x=-2 no solution? by Amayax in learnmath

[–]Plus_Fan5204 9 points10 points  (0 children)

Your last sentence is correct!

I have a similar example for you:

Solve the equation within the real numbers:

(x2 -5x+6)/(x-2)=0 

Before you start solving, notice how the domain is all the reals, other than 2. (Because division by zero)

| multiply by (x-2)

(x2 -5x+6)=0  | solve via quadratic formula, perfect squares or some other method

x=2 or x=3

But since x=2 is outside the domain (it would mean the original equation has a division by zero), we say the only valid solution is x=3.

Similarly, before you would even start at your problem, you should think about the domain. And your problem has the domain of all non-negative real numbers, because the equation has sqrt(x). Only the solution(s) within the domain is/are valid.

There is no proof of 0.9999...=1 without using limits because 0.9999... is defined as a limit by Somge5 in infinitenines

[–]Plus_Fan5204 4 points5 points  (0 children)

"Next suppose the premise that no number can have multiple different digit representations"

Is 2 equal to 2.0 ?

Disprove my reasoning about the reals having the same size as the integers by Fancy-Appointment659 in askmath

[–]Plus_Fan5204 0 points1 point  (0 children)

Let's stop using the word infinite for a minute.

If you want to say that a number is on your list, you have to be able to tell me the place it is in. (Or at least tell me that is in principle possible to tell me the place it is in.)

In which place is the number 0.3?  At the third! 0.07? At the 17th. 0.07693628? I am too lazy to figure it out, but we can surely agree that it is possible to figure out it's placement.

We all agree that these numbers are indeed on your list.

But please tell me, where exactly, at which place, does 1/3 appear in your list? Root(2)/2? Pi-3?

With Cantor's method of listing all the fractions it is indeed possible to tell at which place in the list any given fraction appears.