Assuming something is equal to 1

  • Thread starter gladius999
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In summary, the conversation discusses the concept of assuming a value is equal to 1 in equations and under what circumstances this can be done. It is explained that this assumption is often made because the value is arbitrary and by assuming it is 1, the equation can be solved or a property can be proven. An example is given with the equations a+2b+c=d, 2a-b-4c=d, and a-c=d where d can be assumed to be 1 or 0. Another example is given with the gas law equations where certain constants can be assumed to be 1. It is clarified that in general, assuming a value is equal to 1 is not possible, but in physics, it can be done
  • #1
gladius999
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I have always seen people solving equations while assuming something is equal to 1 (usually a constant). Why and under what circumstances can you assume this? what equations are still valid after u assume that it is 1?

Thanks
 
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  • #2
Post an example, and we can explain why it's a good assumption. Usually you assume a value is equal to 1 because it could be anything (not that you don't know what it is, but that it's arbitrary) and then by assuming it's 1, you can prove that it doesn't satisfy a property for any arbitrary value
 
  • #3
a+2b+c=d
2a-b-4c=d
a-c=d

u can assume d=1?
 
  • #4
Ok, good example. You actually have to break this up into two cases:
1) d=0. If d=0, you can just solve the equation since there are three equations and three unknowns.

2) d =/= 0. If d is non-zero, divide both sides of every equation by d. Call A=a/d, B=b/d, C=c/d. Then we get A+2B+C=1, 2A-B-4C=1, A-C=1 Then every solution of (A,B,C) corresponds to a set of solutions (Ad,Bd,Cd,d) where d is arbitrary. So we can essentially assume that d=0 or d=1 since we can derive all the solutions from this
 
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  • #5
hmm i seem to understand number 1)
but 2) i don't get how u can divide both sides of every equation by zero.

another gas example:
P1V=n1RT1
P2V=n1RT2

where V and R are constants

when solving equations can u assume V and R is 1?
 
  • #6
Well R is a constant. It's the gas constant but if in the specific situation you're looking at the volume doesn't change then you can say n1RT1/P1=V and n2RT2/P2=V therefore you can say n1RT1/P1=n2RT2/P2. as for Office Shredder's post when he said "If d is non-zero, divide both sides of every equation by zero" he actually meant "If d is non-zero, divide both sides of every equation by d". I suspect he just had a brain fart and the fingers typed something different then he was thinking.
 
  • #7
Yeah, that was just a mistype. I fixed my post to reflect what you should actually do
 
  • #8
thnx for ur quick reply guys, i will try apply ur ideas into my thinking:)
 
  • #9
You cannot, in general, "assume something is equal to 1". But if you are talking about measured quantitities in physics, you often can assume a system of units so that value is 1 of whatever units you are using. For example, in the standard "meter-seconds" system, the speed of light is 299,792,458 meters per second. But can, just as well take "the distance time travels in one second", one "light second", to be my distance unit rather than the meter. In that case, the speed of light is 1 "light second per second".
 

1. What does it mean to assume something is equal to 1?

Assuming something is equal to 1 means that you are using the value 1 as a starting point or reference point for your calculations or experiments. It does not necessarily mean that the value is actually equal to 1, but rather that you are treating it as such for the purpose of your scientific inquiry.

2. Why is it common to assume something is equal to 1 in scientific research?

Assuming something is equal to 1 can simplify complex equations and make them easier to solve. It also allows for easier comparison and interpretation of results when using a standardized value. Additionally, some scientific theories or models are based on the assumption that certain variables are equal to 1.

3. Can assuming something is equal to 1 lead to inaccurate or biased results?

Yes, assuming something is equal to 1 can potentially lead to inaccurate or biased results if the value chosen is not an accurate representation of the actual value. It is important for scientists to carefully consider and justify their assumptions in order to minimize potential errors in their research.

4. Are there any alternative values that can be used instead of assuming something is equal to 1?

Yes, there are alternative values that can be used instead of assuming something is equal to 1, such as using a different reference point or using a range of values instead of a single value. The choice of value will depend on the specific research question and the variables involved.

5. How does assuming something is equal to 1 impact the validity of scientific findings?

The impact of assuming something is equal to 1 on the validity of scientific findings depends on the accuracy and appropriateness of the chosen value. If the value is an accurate representation of the actual value, then it may not significantly impact the validity of the findings. However, if the value is not accurate, it may introduce errors or biases that can affect the validity of the results.

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