Zero/Zero questions and perhaps faulty logic So 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,(xy)/(xy)=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 0(x)=0 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

Kade Reese 2022-07-23 Answered
Zero/Zero questions and perhaps faulty logic
So 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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Answers (1)

Raul Garrett
Answered 2022-07-24 Author has 14 answers
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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