[at-l] algebra Re: Facts

[KGJ]

hm.  well, is not 8 but one of the possible square roots of 64, the other being -8 ?  
______________________________________________
"I'll leave the doomsaying to others, I'm too busy working on the future" 
Ed Jones, 2009
_______________________________________________

  ----- Original Message ----- 
  From: David Addleton 
  To: KGJ 
  Cc: Tom McGinnis ; at-l at backcountry.net 
  Sent: Tuesday, April 21, 2009 10:59 PM
  Subject: Re: [at-l] algebra Re: Facts


  the equivocation arises from the word description vs the operational symbols used in mathematics

  "any square root" doesn't *necessarily* mean "√x" -- which refers to a particular operation or procedure to obtain a number while also referring to a particular number; "any square root" can also mean "any number": for example, 8 qualifies as one of "any" of the possible square roots ["any square root" the words literally say] -- the square root, in this instance, of 64. Squared, eight is not itself, but rather, due to the operation or procedure of squaring, it equals sixty-four. The equivocation arises because words are not so precise as to convey whether the speaker means an operation or an identity. Now, it's true that the square root of 64 equals eight and, when squared, eight equals sixty four; but we cannot correctly write or say "the square root of 64" *is* "eight" when we actually mean that a specific operation designed to produce a peculiar and specific factor of 64 produces a number equal to eight.

  so much for mathematical facts described with words . . . 

  or, as George Santayana once correctly wrote: "Whenever I use the word *is* I deeply misuse it."




  On Tue, Apr 21, 2009 at 4:54 PM, David Addleton <dfaddleton at gmail.com> wrote:

    ya n i forgets distinctions between integers and numbers . . . ;)

    On 4/21/09, KGJ <jplynch at crosslink.net> wrote:
      The square of a number, positive or negative, is positive, that is true.  However, the square root of a positive number (as in the equation that I posited based on the earlier email) has two answers, positive and negative.  Hence the need for the absolute operator to make it "true".
      ______________________________________________
      "I'll leave the doomsaying to others, I'm too busy working on the future" 
      Ed Jones, 2009
      _______________________________________________

        ----- Original Message ----- 
        From: Tom McGinnis 
        To: David Addleton ; KGJ 
        Cc: at-l at backcountry.net 
        Sent: Tuesday, April 21, 2009 2:05 PM
        Subject: Re: [at-l] algebra Re: Facts

         


        --- On Tue, 4/21/09, KGJ <jplynch at crosslink.net> wrote:
         
        > uh. is not abs(sqrt[x**2]) not always equal x for 
        > all x>0? is this not a mathematical truism? 

        > -- From: David Addleton 
        >   don't drink 'n derive: I beg to differ:  
        >   that "the square of any square root is
        > itself" is true *only* in the *single* case of *one*

        1) You are indeed correct, Prof. Lynch -- a mathematical truism, but to an even more general case, that being all numbers positive or negative. Thus, the "abs" in your equation is, strictly speaking, not necessary. (The square of a negative number is positive.)

        2) I wish I could claim originality here, but I just went through this area in my algebra class, except I taught it as "Girls take time and money..." You can guess the rest. Always think I'm kidding until they see the test.....



        plagaristoe


        Oh! And 3)
        FWIW (Counselor Addleton), "1" is not the loneliest number. Positive numbers have two roots (a positive and a negative), while negative numbers are split into positive equivalents and multiplied by negative 1. (Thus, √-2 = √2*√-1) When you get to the square root of negative one, *then* you have one of the mathematical special cases that launch new branches -- in this case "complex numbers" -- being products of real numbers and imaginary numbers. The square root of -1 is the start of all that:

           √-1 = i, and i² = -1

        and "i" is, of course, the imaginary number.

        Don't it just bring ya back?

        To make this hiking related, I THINK this means that if we do virtual hiking, internet hiking, screen slide shows, etc? I think (THINK) this means that we undo our otherwise "real" hiking miles with our "imaginary" hiking miles. This would also explain the growth of my belt size, buffet-proximity-rule or not. Dang.

        AYCEismetoe





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