Zero/Zero questions and perhaps faulty logicSo I only have an Algebra II level understanding of math seeing as I am still in high school and am still missing some fundamentals seeing as I didn't pay attention in math until this year. However when recalling something my algebra teacher had taught me during the year I came up with some questions regarding the logic recently.So during the school year, I was taught that 2 2 = 1 , a a = 1 , x y x y = 1 and so forth but 0 0 = Undefined... and while researching this topic I found that the algebraic way to write all these fractions is as such 2 ( x ) = 2 , a ( x ) = a , and upon researching this further I found that the reason that 0 0 is undefined is that for any value of x the equation holds true. However, seeing as in the fraction a a a is a variable and variables can represent any given quantity I was wondering in the case that a = 0 would a a still = 1 and if not why along with the fact that lets say a = 0 and you didn't know it why is it safe to assume that a would never equal zero? Also if it happens to be the case where when a = 0 , a a = 1 (which I doubt it is) shouldn't this mean that 0 0 = 1 then?

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Zero/Zero questions and perhaps faulty logicSo I only have an Algebra II level understanding of math seeing as I am still in high school and am still missing some fundamentals seeing as I didn&#039;t pay attention in math until this year. However when recalling something my algebra teacher had taught me during the year I came up with some questions regarding the logic recently.So during the school year, I was taught that       2    2    =  1  ,      a    a    =  1  ,            x      y              x      y        =  1 and so forth but       0    0    =  Undefined... and while researching this topic I found that the algebraic way to write all these fractions is as such   2  (  x  )  =  2  ,  a  (  x  )  =  a  , and upon researching this further I found that the reason that       0    0   is undefined is that for any value of   x the equation holds true. However, seeing as in the fraction       a    a     a is a variable and variables can represent any given quantity I was wondering in the case that   a  =  0 would       a    a   still   =  1 and if not why along with the fact that lets say   a  =  0 and you didn&#039;t know it why is it safe to assume that   a would never equal zero? Also if it happens to be the case where when   a  =  0  ,      a    a    =  1 (which I doubt it is) shouldn&#039;t this mean that       0    0    =  1 then?

Raul Garrett · Accepted Answer

a    a    =      {                            1                          a          ≠          0                                      undefined                          a          =          0                        Strictly speaking, you have to check whether   a is zero before you cancel terms off from both numerator or denominator.Even before we write down       a    a  , we should first check if the denominator can be zero, i.e. check it before we write down such term.

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