We have: a = xut, b = xut, c = yut y = 2x a, b and c are periods of time. ut are units of time. x and ut are independent variables. Case 1: Between a and b It may be that: a = b, a > b, b > a Case 2: All ut and x are equal. c > a and b Case 3: b = 10a, same ut. b > a Case 4: What would it happen if in case 3 the ut are different? Asexperia
Statement is confusing. a and b have the same definition. Is ut a single variable? Using two letters is confusing - usually it stands for a product of two variables.
This thread has nothing to do with time, by the way. It looks sort of like basic maths dressed up in a confusing way.
I'm going to attempt to put this into a more standard form. Let $t$ be a time interval. For example $t$ could be 1 hour or 1 year or 1 second. Now define $a = xt, b=xt, c=yt$. With $y=2x$ we also have $c=2xt$. What's between a and b? You're not making sense. So far, we have $a=b=xt$. $a$ and $b$ are equal, by definition. No. It can only be that $a=b$, given the definitions at the start. Are you now saying that $x$ is a time interval, like $t$? In that case $a,b$ and $c$ would be squared time intervals. Are you saying $x=t$? In that case $a=b=t^2, c=2t^2$. Correct. Impossible, since it conflicts with previous definition that $a=b$. Impossible. Nothing. Case 3 is impossible.
You defined a as equal to b so, it is incorrect to now say a > b. Maybe you should not try to use math and go back to just hand waving.
Right the time can be different. But your base equation still says a equals b. a = xt = b therefore a = b.
So x and z are just numbers with no physical significance? There is no possible way to know which is higher or lower for a, b, or c based on the information given.
Since x and z are both just numbers you can simplify this by using just x OR z. Let's just use x. It seems like you are saying that the s, m, h and y are just the units. If that is the case you should just use a single unit to simplify the equations. If you just use seconds then your first 2 equations are now a = x = b or just a = x. Since a = x we can just use a. So if a0 is 1 and a1 is 60 then a1>a0. This doesn't really seem to be saying anything that isn't intuitively obvious to the most casual observer.
The equation of time represents any measure of time no matter if it is in seconds, minutes, hours or years. Everyone knows that a measure is made up of a number and a unit of measure. In these equations a custom letter is assigned to the measure. An example: d = xy. d can be the age of any person.
You do not have an equation of time. Your 'equation' basically says a = some amount of time, not really an equation just a substitution. Right, in SI units time is seconds, trying to put units in the equation with an arbitrary constant is unnecessary and an incorrect way to write a math equation. Your example should be d = 25 years, for example. d = xy is nonsense, it is a waste of time to say x =25 and y = years when you could just say 25 years. Your attempt at the math adds nothing except confusion.