/sci/ - Science & Math

>>5126138
Still reading through this, about half-way through.

>>5126155
What do you mean the first part?

>>5126093
I'm trying as hard as I can. I focus on what I'm reading and try to make sense of it. I mean I read the proof and I can see that it proves that for x^a to be the same as \sqrt[n]{x}, a must be 1/n, and therefore \sqrt[n]{x} = x^1/n, but I don't get how "since (x^a)^b=x^(a*b) it's pretty clear, why \sqrt[n]{x}=x^{1/n}".

>>5126022
Yes, I went through the proof and could see that each step worked out. But I don't get it.

>>5125906
OK I still haven't gotten why a number to the power of a fraction is the same as the denominator root of that fraction by it's numerator.
I just can't get why

>since (x^a)^b=x^(a*b) it's pretty clear, why \sqrt[n]{x}=x^{1/n}

>>5125846
OK so 1=1^a so 1/x^a is (1^a)/(x^a)

and that is the same as 1^a by the inverse of x^a, which is x'^a

Multiplying those two is just x'^a, which is (1/x)^a

How did you do all those steps so quickly to get from 1/(x^a) to (1/x)^a?

>>5125821
I guess because they aren't so weak that they are scared of the regulars and do exactly as they say, and also fold under questioning?

>>5125771
What is x^a? I've been reading this for over 20 minutes and I don't get it.

>>5125849
>1/(x^a)=(1^a)/(x^a)
How does that work?

>>5125762
So that is right because 1/(x^a) = (1/x)^a? What is that called?

>>5125750
>lets say, c' is the multiplicative inverse of c
>a*b/c*d = a*(b*c')*d=(a*c'*d)*b=(a/c*d)*b
>we can do this, because multiplication on the real numbers is commutative (a*b=b*a) and associative (a*b)*c=a*(b*c)
It took me 10 minutes but I finally got this. I had to take the b/c = b*c' part at face value or for granted (however you say that) because I still don't fully understand that and the 'associative' part confuses me a little but I got it.

>>5125750
>I know. It seems to be a bit of an unintuitive approach to tackle the problem. But it's way better than seeing multiplication as repeated addition and all that crap (because that doesn't work well on irrational numbers).
>Also it prepares you for higher math
Yeah, I really appreciate your time and effort. I got the one I said I was getting there to based on the principles above. I'm now trying to get >>5125762

>>5125686
>since (x^a)^b=x^(a*b) it's pretty clear, why \sqrt[n]{x}=x^{1/n}
I don't get how (x^a)^b=x^(a*b) leads to \sqrt[n]{x}=x^{1/n}

>>5125686
>1=x^0=x^{a-a}=x^{a+(-a)}=x^a*x^{-a}
>that implies, that x^(-a) is the multiplicative inverse of x^a
That makes sense. But why does that lead to x*-a = 1/x^a?

>>5125686
>let b' be the multiplicative inverse of b and d' be the multiplicative inverse of d
>than (a/b)*(c/d)=(a*b')*(c*d') . since multiplication is a commutative and distributive operation on the real numbers we can do the following step:
>(a*b')*(c*d')=(a*c)*(b'*d')=(a*c)/(b*d)
It's taking me a long time to get this but I think I'm getting there.

>reading this gave me a headache, sorry
I mean like a*b/c*d = (a/c*d) x b. I didn't get a video on gravity because of this.

>>5125684
OK sorry, I got the numbers mixed up.

>>5125621
>and lets say (q is the reciprocal of k ) then q.13 = q. k .11 but q.k =1
Are you saying that what you said before q.k=1 showed why q.k=1, or is that just a part of what you are showing?

>so q.13 = 11
What are the implications of this?

>>5125672
I did pay attention to that.

>>5125664
I'm not getting this exactly. If a/b=n, then a=bn and b=a/n, so ab=bn(a/n).

>>5125621
>The reason why its 11/13 is because lets say 13/11 = k, then 13=k .11
so 13 = 13/11x11 ? 13 = 13/121?

>>5125611
>Reciprocals are simply a number flipped, which is why you have the same number on both sides of the fraction line. The reciprocal of 23/555 would be 555/23, and both sides are 555*23 or 23*555, which is the same number, which is then divided by itself, which is then 1.
A lot have provided this explanation, but I'm still in the process of understanding why 23/555 x 555/23 = 23x555/555x23.

>>5125603
What difference does that make?

>>5125599
>Yeah, that's correct. We can simplify that to being (24/5)/7. We can then say this equals to:
>
>(24/7)/5
I did not know this. Is this another rule?

>>5125599
>Now, we can multiply both the numerator and the denominator by 7 to make this look nicer.
>
>(24/7)*7 / (5*7)
>=24/35

So is this the logic behind 4/5 x 6/7 = 4x6 / 5x7?

>>5125568
I get that but I don't get why something like 13/11 x 11/13 = 1.

>>5125572
>I could also ask you why 0 . x=0, it seems obvious but it's impossible to demonstrate with elementary math.
I thought it was because nothing of x equals nothing.

>>5125549
I understand the maths when it's 1 as the numerator of one fraction and 1 as the denominator of the other, but what about 7/9s of a cake split up into 9/7 slices?

>>5125555
>A reciprocal is just 1 divided by some number. 1 divided by some number, multiplied by the EXACT same number must equal 1.
Yeah, that's what I don't understand. Why does the reciprocal of a number multiplied by that EXACT number equal 1?

>>5125555
>Say you have 4/5 of a pie. You are then ordered to take 6/7 of what is there. 6/7 is the same thing as multiplying by 6, then dividing by 7. Therefore, the new fraction of what you have becomes (4*6)/(5*7), which is 24/35
How did you jump from 4/5 x 6 then divided by 7 to (4*6)/(5*7)? Wouldn't 4/5 x 6 and the number divided by 7 be (4/5x6)/7? Or ((4x6)/5)/7?

>>5125547
So you are saying the understanding of why a number by its reciprocal equals 1 is not elementary?

>>5125529
>Well, if it works for thirds, then try it with fourths, then fifths.
For fifths, 5 wholes of 1/5 = 1. I think I understand 1/3 because I understand all of them that have a 1 in the denominator of one of the fractions and the numerator of the other.


>N is ANY NUMBER, we can see that N multiplied by its reciprocal ( which is 1/n ) is equal to n/n well, anything divided by itself is one.
>
>So we have shown that N, which is also ANY NUMBER, multiplied by its reciprocal is the same as N / N or ANY NUMBER divided by ANY NUMBER, hence divided by itself, which is always 1.
I don't understand the first part of that (question 3) in the first place to understand that as an explanation if I could.

>>5125523
I'll answer this when I'm finished googling all the terms and figuring out what they mean. The first one was "operation sum", the first result of which was "summation" on wikipedia. I hope this is the right place, is it?

>>5125514
>Just so you know, those lines in my picture weren't necessarily related to eachother, they were just various lines of rules and examples that make sense, sorry if you thought they were in an order or something.
I did think this but now I'm corrected

>>5125514
>You must understand the last example on that picture on the right, surely. that three thirds added together is one whole, i.e 1.
Yes, I understand that part, I understand that three 1/3s are 1 and therefore 3/1 multiplied by its reciprocal 1/3 equals 3, but I don't understand why all fractions by their reciprocal equal 1.

>>5125501
You explained what I don't understand with what I don't understand either.

>>5125496
I don't get the picture. How does it jump from the first three lines to the fourth?