Multiplying with variable

Ryan$

Full Member
Joined
Jan 25, 2019
Messages
345
Hi guys!
I have a missunderstanding of wha's going while mulilpying my equation/formula with variable or divide by variable, I'm now to trying to troll or kidding, I want to learn why it's right , so PLEASE bear me and my ears now are really want to learn, no more nothing else.

I've a struggle when my teacher do like this :
there's a formula := I = U /R Im totally understand this, now my problem is when my teacher write I=(U/R) * U/U is the same as I=U/R and he just multiply by 1, what's confusing me that U might be zero, so he didn't mention that case and also other teachers just multiplying/dividing a formula with variables without clarifying that this variables can't be zero ..

my question is , is it right to multiply U/U on formula I=U/R without saying that U can't be zero? because if it's zero then we cant do U/U ... must I mention once I muliply and divide by variable that this variable can't be zero? about all teachers conventionally forgetting from putting a note that the variable we multiply and divide by it can't be zero .. so is it right to not sign that note while multiplying and dividing with the same variable?

I'm confusing why we didn't mention while multiplying and dividing with same variable that this variable can't be zero .. otherwise we can't do U/U because U might be zero (U is variable)

thanks
 

lev888

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Jan 16, 2018
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Yes, we need to note that U can't be zero. Maybe it's clear from the context that U can't be 0?
 

Mr. Bland

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Dec 27, 2019
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105
In a formal sense, it should be noted that \(\displaystyle U \ne 0\) due to the potential for zero division. Your teacher was demonstrating that a fraction in the form of \(\displaystyle \frac{x}{x} = 1\), which of course doesn't apply to zero anyway because \(\displaystyle \frac{0}{0}\) isn't a valid fraction.

In other cases, such as \(\displaystyle \left(\sqrt{x}\right)^2 = x\), it's important to understand that there is a range of valid possibilities, but depending on the context it may be inconvenient or "too wordy" to spell it all out every time. The focus is the on relationship between \(\displaystyle \sqrt{x}\) and \(\displaystyle x^2\), not on the fact that \(\displaystyle \sqrt{x}\) expects and returns non-negative values.
 

Ryan$

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Jan 25, 2019
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345
Yes, we need to note that U can't be zero. Maybe it's clear from the context that U can't be 0?
that what I want to verify, if from the context it's clear that we are not meaning 0/0 .. then we can not writing a note that variable can't be zero over variable/variable? if from context we can assume that and this assumption is logically considered right, then fine for me and now it's obvious why they are neglecting a note when dividing X/X or VARIABLE/VARIABLE
 

JeffM

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Sep 14, 2012
Messages
4,334
that what I want to verify, if from the context it's clear that we are not meaning 0/0 .. then we can not writing a note that variable can't be zero over variable/variable? if from context we can assume that and this assumption is logically considered right, then fine for me and now it's obvious why they are neglecting a note when dividing X/X or VARIABLE/VARIABLE
I still think it is a bit sloppy
 

mmm4444bot

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… is it right to multiply U/U on formula I=U/R without saying that U can't be zero? …
What did your teacher say, when you asked them that question?

\(\;\)
 

Jomo

Elite Member
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Dec 30, 2014
Messages
5,407
Students always say that x/x = 1, which is not true--end of discussion. I tell them that x/x is a piecewise function which is .....

Fair enough if it is obvious that U \(\displaystyle \neq\)0 then one can get away without saying that U \(\displaystyle \neq\)0 when multiplying by U/U. Otherwise it is sloppy not to mention it. I have this obsession that equal signs MUST be valid and when they are not your work is not (completely) correct.
 
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