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1. ### B Relation between Division and multiplication

@fresh_42 This totally is the case. I agree with you and Feynman. People here don’t explain in simple language and pour lots of information as a reply. This makes hard to understand and then they say we have pointed this or that out many times but you ignored. I don’t ignore. It gets lost into...
2. ### B Relation between Division and multiplication

I saw. and this proves my point. “Vast majority” always do what’s convenient. They would not understand inverse of a. Same thing with percentage. People understand 100. They are able to Compare things with 100. That’s why we use percent today. That’s a mistake or typo.
3. ### B Relation between Division and multiplication

Isn’t everything just addition? Subtraction is addition of opposite. Multiplication is repeated addition and division is just opposite of multiplication which is also just addition.
4. ### B Relation between Division and multiplication

Just because division is used by companies with big names doesn’t qualify division as a concept. It’s still multiplication. They must have used it because its convenient. Division has made life easier.
5. ### B Relation between Division and multiplication

It’s for convenience that we teach division to kids. Actually what we are doing is inverted multiplication. That’s what he meant by “to give all kids same number of cookie”. Division is for convenience.
6. ### B Relation between Division and multiplication

If we are literally breaking down things into very basics then we are actually doing repeated addition. ##13## added ##13## times =##169##. But we can save time and do direct multiplication.
7. ### B Relation between Division and multiplication

Ok. That is some fresh information. So what I said is right. Yes? (##\frac pq=n## means ##p=qn##)
8. ### B Relation between Division and multiplication

For example what is ##\frac {169}{13} = ?## This says “When ##169## is divided into ##13## groups how many there are in each group?” This can be converted into a multiplication problem like this “##13## groups of how many in each group makes ##169##?” This is ##13 * ? = 169##. It can be solved...
9. ### Algebra Algebra 2 textbook recommendations please

Do I need advanced calculus in higher physics? If so I will buy it.
10. ### Trying to understand the property of absolute value inequality

You sound like I can’t learn maths.
11. ### Trying to understand the property of absolute value inequality

Ok. We define things and combine them to make fundamental statements which can be proved by the definition itself like here. But I am not satisfied that distance definition doesn’t work to prove axiom.
12. ### Trying to understand the property of absolute value inequality

Translation: Axioms are not that difficult to understand. But I don’t know why this one doesn’t feel obvious. By ‘it’ you mean property of absolute value inequality just to be clear.
13. ### Trying to understand the property of absolute value inequality

I There is some miss understanding. Maybe my English. Do you mean ‘##|x|<c## is equivalent to ##-c<x<c##’ as axiom?
14. ### Trying to understand the property of absolute value inequality

You are saying that we cannot prove the property by this definition of distance ##|x-y|## but there are other definitions by which we can.
15. ### Trying to understand the property of absolute value inequality

Can you be a bit more clear in what you are saying ?
16. ### Trying to understand the property of absolute value inequality

So? Show me how can I prove the property by this definition.
17. ### Trying to understand the property of absolute value inequality

Why are you guys only using the definition of ##|x|## ? Why can’t we prove the property ##|x|<c## is equivalent to ##-c<x<c## by considering the fact that ##|x|## is distance between ##0## and ##x## or as I am speculating it as distance between ##0## and ##-x## ? It seems like you are saying...
18. ### Trying to understand the property of absolute value inequality

Is ##| |## a notation on ##x## which means ##x## or ##-x## depending on the value of ##x## ? Like the notation ##x^n## means ##x.x…x## (n terms).
19. ### Trying to understand the property of absolute value inequality

Hello! Good to see you. I don’t know why but I have a desire to write ##|x|## as ##x## which is completely wrong since ##|-5| \neq -5##. If we are not careful it becomes ##x<c##. On a number line ##x## would be left of ##c## up to ##-\infty## , if ##c>0##. This doesn’t match with the book. This...
20. ### Trying to understand the property of absolute value inequality

If ##x \geq 0## , ##-c<x<c## means ##|x|<c## If ##x<0## , ##-c<x<c## means ##|x|<c## So ##|x|<c = -c<x<c## Can you answer this please (post # 8) ?
21. ### Trying to understand the property of absolute value inequality

If ##x>0## then ##|x|<c## means ##x<c## If ##x<0## then ##|x|<c## means ##x>-c## So for all ##x## , ##|x|<c## means ##-c<x<c## (##x## lies between ##-c## and ##c##).
22. ### Trying to understand the property of absolute value inequality

##|x|## means distance between x and 0. But I am thinking we can also write ##|x|=|0-(-x)|## which means it is the distance between 0 and -x. Am I right?
23. ### Trying to understand the property of absolute value inequality

Ok. 13 can be written in infinite ways. ##|0-13|## , ##|0-(-13)|## , ##|5-(-8)|## , ##|-2-11|##. Similarly if ##x## is a variable in place of a number then ##|x|## is the distance between 0 and x. But how do we add ##-x## to the story to prove ##-c<x<c##?
24. ### Trying to understand the property of absolute value inequality

First lets focus on ##|x|## which is defined as distance between ##x##and ##0##. But if we look into it closely $$13=|-11-2|$$ which is distance between -11 and 2 but $$13=|11-(-2)|$$ which means this is distance between 11 and -2. Which is it? In the same way $$x=|x-0|$$ is distance between 0...
25. ### Intro Math Wanting to study Functions from scratch for my Calculus preparation

But I asked one question regarding books. That’s a relief. I prepare myself that now I’ll complete this or that book and will pursue my journey to learn science. I start the book and then I leave because the math is above my level. So I go buying new book. And then this cycle repeats. I start...
26. ### Intro Math Wanting to study Functions from scratch for my Calculus preparation

Actually I want to revise algebra 1 and 2 and move forward. Learn new maths. But I don’t want to buy new book. I was thinking if this book will do the job for a while? (I am tired of buying books)
27. ### Intro Math Wanting to study Functions from scratch for my Calculus preparation

Function that is taught in algebra I and II I suppose.
28. ### Intro Math Wanting to study Functions from scratch for my Calculus preparation

Does Precalculus by James Stewart teaches function from scratch ?
29. ### Solving Equations: Does Squaring Make False True?

Is it possible to find the solution of ##2x-1=-\sqrt {2- x}## in the start without squaring? I mean we know the solution of ##x=-1## is ##x=-1## at the start. So it would be good if we declare the solution of the original equation in the beginning if we are doing analogies.
30. ### Solving Equations: Does Squaring Make False True?

By the way in post #9 I factored eqn ##1## (##(2x-1)^2=2- x##)by splitting the middle term and eqn ##2## (##x^2=1##) by the factoring formula ##A^2-B^2##. I don't think that will make any difference how we factor.
31. ### Solving Equations: Does Squaring Make False True?

I like when I am able to see in those complicated equations what simple things are going on in terms of ##x## and ##y##.
32. ### Solving Equations: Does Squaring Make False True?

Actually I was searching for you, person whom I can understand because they are talking in the same language as my current maths book. So it becomes very easy to follow up. I don't understand much when people talk in high level language. You know what that means. HaHA :)
33. ### Solving Equations: Does Squaring Make False True?

I mean my all lines are right especially where I said ##2x-1## can be taken as ##x## and ##2-x## is ##1##?
34. ### Solving Equations: Does Squaring Make False True?

Please verify each step so that I am sure I understood it in depth and not superficially.
35. ### Solving Equations: Does Squaring Make False True?

Let me give it a try. Lets take ##x=-1##. I added -ve sign to make it analogous to our original equation ##2x-1=-\sqrt {2- x}## ##2x-1=-\sqrt {2- x}## equivalent to ##x=-1=-\sqrt 1## (Here ##2x-1## expression is ##x## and ##2-x## expression is ##1##) Solution: x=-1/4 and...
36. ### Solving Equations: Does Squaring Make False True?

I don’t understand. I am asking how are extraneous solutions introduced? Does anyone get what I am saying?
37. ### Solving Equations: Does Squaring Make False True?

Does this mean for x=1 , ##2(1)-1= -\sqrt{2-1}## is false. x=1 is not a solution. But as we square the above equation , ##(2(1)-1)^2=(-\sqrt{2-1})^2## , false equation becomes true. So now x=1 is solution to the new equation ? (Here is the paragraph attached) from book James Stewart.
38. ### Problems in manipulating these 4 radical equations

I am given an equation to solve and I am unable to understand why definition of root doesn’t work both ways. Namely if ##\sqrt 5 = x## means ##x^2=5## then ##x^2=5## doesn’t means ##\sqrt 5=x## It has to do with root and square. Square having unique value but root gives two values. But I don’t...
39. ### Algebra Algebra 2 textbook recommendations please

James Stewart. Yeah! I think I need that.
40. ### Algebra Algebra 2 textbook recommendations please

I do fear that if I don’t go in linear fashion I’ll get stuck in future. I have precalculus book in paperback. I will continue with it for now. Thanks!
41. ### Problems in manipulating these 4 radical equations

That I missed. Good point. And now I understand that ##(\sqrt{2x+1})^2= ({2x+1})^{\frac 12(2)}= 2x+1##. In this part ( ##x^2=5##) why can’t I just use the definition of radicals ?
42. ### Problems in manipulating these 4 radical equations

Yes, So we can’t just cancel the powers. ##\sqrt {(-4)^2}= 4##. How come then ##(\sqrt{2x+1})^2= \sqrt{(2x+1)^2}=2x+1##?
43. ### Problems in manipulating these 4 radical equations

In order to write next step in all four equations above l used the definition of radicals. ##\sqrt a=b## means ##b^2=a##. Squaring both sides also works. I don’t know if it’s right. I mean I read that ##(\sqrt a)^2=a##. But I don’t know if we can apply this on expressions. Main problem is if we...
44. ### Algebra Algebra 2 textbook recommendations please

Can you provide me pdf link to the book? I can’t find one.
45. ### Algebra Algebra 2 textbook recommendations please

I have an urgent need to clear my concept on solving equations involving radicals. Does any of those books have that? If not please specify one!
46. ### Algebra Algebra 2 textbook recommendations please

I read that somewhere. Thank you. That will save a lot of money :)
47. ### Algebra Algebra 2 textbook recommendations please

I am currently learning some maths from “Precalculus by James Stewart”. I was wondering if that’s ok? Is it ok to just dive straight into it or go back and brush up my algebra 2 ? I was wondering what are some good textbooks on algebra 2 by the way? Thank you. (This is all for the love of physics).
48. ### Identifying the type of expression

What about ##(x^2+3)^{-\frac13} + \frac23 x^2(x^2+3)^{-\frac43}## ? Fractional expression? or this ##(x^2+3)^{-\frac13} + 2 x^2(x^2+3)^{-\frac43}## ?
49. ### Identifying the type of expression

Thanks man :)
50. ### Identifying the type of expression

TL;DR Summary: ##(1+ \frac1x)^2 - (1-\frac1x)^2## ##(z+2)^2 -5(z+2)## Upon simplifying the first I get ##\frac4x##. So isn’t the first expression fractional? Upon simplifying the second I get a Quadratic expression.