Mixing
Equations and their Transformations [closed]
Clash Royale CLAN TAG#URR8PPP
up vote
-2
down vote
favorite
I am working on a mathematical theory on infinites, injective functions, and the like, and I need to know something about equations. This question is obvious from my mathematical background, but I need to have the question answered for all possible forms of math, and know it's boundaries.
Here is an equation:
5x+3=9
If I was solving the equation, and for whatever reason wanted to multiply the LHS by 5, is there ANY exception that it won't be the same equation if I multiplied the RHS by 5?
I am asking this for EVERY possible type of equation, anything with that looks like LHS=RHS.
If there are certain boundaries, can you explain them? For example, if they do not apply to a certain type of differential equations in the 7447th dimension or vector equation, please let me know!
Also, on a tangent: there should be a tag for theories or general equations.
Edit: I'm going to stop wasting my time now. Answer this:
Is there a way to categorize or a known categorization of whether transforming(doing ANY type of math to an equation) keeps it proportional?
soft-question
asked Jul 30 at 21:10
Shadow Sniper
85
closed as unclear what you're asking by zipirovich, amWhy, Leucippus, Jyrki Lahtonen, Taroccoesbrocco Jul 31 at 8:30
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
 |Â
show 5 more comments
up vote
-2
down vote
favorite
I am working on a mathematical theory on infinites, injective functions, and the like, and I need to know something about equations. This question is obvious from my mathematical background, but I need to have the question answered for all possible forms of math, and know it's boundaries.
Here is an equation:
5x+3=9
If I was solving the equation, and for whatever reason wanted to multiply the LHS by 5, is there ANY exception that it won't be the same equation if I multiplied the RHS by 5?
I am asking this for EVERY possible type of equation, anything with that looks like LHS=RHS.
If there are certain boundaries, can you explain them? For example, if they do not apply to a certain type of differential equations in the 7447th dimension or vector equation, please let me know!
Also, on a tangent: there should be a tag for theories or general equations.
Edit: I'm going to stop wasting my time now. Answer this:
Is there a way to categorize or a known categorization of whether transforming(doing ANY type of math to an equation) keeps it proportional?
soft-question
asked Jul 30 at 21:10
Shadow Sniper
85
closed as unclear what you're asking by zipirovich, amWhy, Leucippus, Jyrki Lahtonen, Taroccoesbrocco Jul 31 at 8:30
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
The question is really general but as a simple example if we consider $x=1$ and multiply by $x $ we obtain $x^2=x$ which is a different equation since in the latter case the solutions are $$x^2-x=0 iff x(x-1)=0 iff x=0 lor x=1$$. But it is the same equation, as it should be in a proper manipulation, if we take $xneq 0$ when multiply by $x$.
– gimusi
Jul 30 at 21:17
If you're curious, my theory involves using transformations on equations using a new type of number that multiplies it by every possible number, creating a large set of equations from each one. Then, with all the possibilities, we scale them back down using a different method that reserves the original equation but in a different form of equations that I am creating which allows for infinite algebra.
– Shadow Sniper
Jul 30 at 21:18
So based on what you're saying, what forms of equations/functions do not allow transformations to remain the same? I am certain that most equations/functions with powers do not allow it, and also logs and possibly radicals, since they are negative powers. Would trigonometric equations preserve? Circles continue to repeat, even though they can be simplified. For example, multiplying 360 degrees by 2 is 720, but it is still geometrically 360 degrees.
– Shadow Sniper
Jul 30 at 21:26
Your claim is to much general in that way, maybe you could consider some concrete example to discuss here.
– gimusi
Jul 30 at 21:31
If by concrete you mean real-life situation, I can give you one. So the amount of money John makes an hour is represented in this equation: 5x+35=67. If John's boss halved the equation, would his income in half the time be proportional? i.e., since the equation was split in half, does a value of x/2 result in a proportional answer? You can solve that, check it, blah blah. So what I'm asking is, for what types of equations or functions does that type of reasoning not remain true?
– Shadow Sniper
Jul 30 at 21:33
 |Â
show 5 more comments
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
I am working on a mathematical theory on infinites, injective functions, and the like, and I need to know something about equations. This question is obvious from my mathematical background, but I need to have the question answered for all possible forms of math, and know it's boundaries.
Here is an equation:
5x+3=9
If I was solving the equation, and for whatever reason wanted to multiply the LHS by 5, is there ANY exception that it won't be the same equation if I multiplied the RHS by 5?
I am asking this for EVERY possible type of equation, anything with that looks like LHS=RHS.
If there are certain boundaries, can you explain them? For example, if they do not apply to a certain type of differential equations in the 7447th dimension or vector equation, please let me know!
Also, on a tangent: there should be a tag for theories or general equations.
Edit: I'm going to stop wasting my time now. Answer this:
Is there a way to categorize or a known categorization of whether transforming(doing ANY type of math to an equation) keeps it proportional?
soft-question
asked Jul 30 at 21:10
Shadow Sniper
85
I am working on a mathematical theory on infinites, injective functions, and the like, and I need to know something about equations. This question is obvious from my mathematical background, but I need to have the question answered for all possible forms of math, and know it's boundaries.
Here is an equation:
5x+3=9
If I was solving the equation, and for whatever reason wanted to multiply the LHS by 5, is there ANY exception that it won't be the same equation if I multiplied the RHS by 5?
I am asking this for EVERY possible type of equation, anything with that looks like LHS=RHS.
If there are certain boundaries, can you explain them? For example, if they do not apply to a certain type of differential equations in the 7447th dimension or vector equation, please let me know!
Also, on a tangent: there should be a tag for theories or general equations.
Edit: I'm going to stop wasting my time now. Answer this:
Is there a way to categorize or a known categorization of whether transforming(doing ANY type of math to an equation) keeps it proportional?
soft-question
asked Jul 30 at 21:10
Shadow Sniper
85
edited Jul 30 at 21:43
asked Jul 30 at 21:10
Shadow Sniper
85
asked Jul 30 at 21:10
Shadow Sniper
85
asked Jul 30 at 21:10
Shadow Sniper
85
85
closed as unclear what you're asking by zipirovich, amWhy, Leucippus, Jyrki Lahtonen, Taroccoesbrocco Jul 31 at 8:30
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by zipirovich, amWhy, Leucippus, Jyrki Lahtonen, Taroccoesbrocco Jul 31 at 8:30
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
The question is really general but as a simple example if we consider $x=1$ and multiply by $x $ we obtain $x^2=x$ which is a different equation since in the latter case the solutions are $$x^2-x=0 iff x(x-1)=0 iff x=0 lor x=1$$. But it is the same equation, as it should be in a proper manipulation, if we take $xneq 0$ when multiply by $x$.
– gimusi
Jul 30 at 21:17
If you're curious, my theory involves using transformations on equations using a new type of number that multiplies it by every possible number, creating a large set of equations from each one. Then, with all the possibilities, we scale them back down using a different method that reserves the original equation but in a different form of equations that I am creating which allows for infinite algebra.
– Shadow Sniper
Jul 30 at 21:18
So based on what you're saying, what forms of equations/functions do not allow transformations to remain the same? I am certain that most equations/functions with powers do not allow it, and also logs and possibly radicals, since they are negative powers. Would trigonometric equations preserve? Circles continue to repeat, even though they can be simplified. For example, multiplying 360 degrees by 2 is 720, but it is still geometrically 360 degrees.
– Shadow Sniper
Jul 30 at 21:26
Your claim is to much general in that way, maybe you could consider some concrete example to discuss here.
– gimusi
Jul 30 at 21:31
If by concrete you mean real-life situation, I can give you one. So the amount of money John makes an hour is represented in this equation: 5x+35=67. If John's boss halved the equation, would his income in half the time be proportional? i.e., since the equation was split in half, does a value of x/2 result in a proportional answer? You can solve that, check it, blah blah. So what I'm asking is, for what types of equations or functions does that type of reasoning not remain true?
– Shadow Sniper
Jul 30 at 21:33
 |Â
show 5 more comments
1
The question is really general but as a simple example if we consider $x=1$ and multiply by $x $ we obtain $x^2=x$ which is a different equation since in the latter case the solutions are $$x^2-x=0 iff x(x-1)=0 iff x=0 lor x=1$$. But it is the same equation, as it should be in a proper manipulation, if we take $xneq 0$ when multiply by $x$.
– gimusi
Jul 30 at 21:17
If you're curious, my theory involves using transformations on equations using a new type of number that multiplies it by every possible number, creating a large set of equations from each one. Then, with all the possibilities, we scale them back down using a different method that reserves the original equation but in a different form of equations that I am creating which allows for infinite algebra.
– Shadow Sniper
Jul 30 at 21:18
So based on what you're saying, what forms of equations/functions do not allow transformations to remain the same? I am certain that most equations/functions with powers do not allow it, and also logs and possibly radicals, since they are negative powers. Would trigonometric equations preserve? Circles continue to repeat, even though they can be simplified. For example, multiplying 360 degrees by 2 is 720, but it is still geometrically 360 degrees.
– Shadow Sniper
Jul 30 at 21:26
Your claim is to much general in that way, maybe you could consider some concrete example to discuss here.
– gimusi
Jul 30 at 21:31
If by concrete you mean real-life situation, I can give you one. So the amount of money John makes an hour is represented in this equation: 5x+35=67. If John's boss halved the equation, would his income in half the time be proportional? i.e., since the equation was split in half, does a value of x/2 result in a proportional answer? You can solve that, check it, blah blah. So what I'm asking is, for what types of equations or functions does that type of reasoning not remain true?
– Shadow Sniper
Jul 30 at 21:33
1
1
The question is really general but as a simple example if we consider $x=1$ and multiply by $x $ we obtain $x^2=x$ which is a different equation since in the latter case the solutions are $$x^2-x=0 iff x(x-1)=0 iff x=0 lor x=1$$. But it is the same equation, as it should be in a proper manipulation, if we take $xneq 0$ when multiply by $x$.
– gimusi
Jul 30 at 21:17
The question is really general but as a simple example if we consider $x=1$ and multiply by $x $ we obtain $x^2=x$ which is a different equation since in the latter case the solutions are $$x^2-x=0 iff x(x-1)=0 iff x=0 lor x=1$$. But it is the same equation, as it should be in a proper manipulation, if we take $xneq 0$ when multiply by $x$.
– gimusi
Jul 30 at 21:17
If you're curious, my theory involves using transformations on equations using a new type of number that multiplies it by every possible number, creating a large set of equations from each one. Then, with all the possibilities, we scale them back down using a different method that reserves the original equation but in a different form of equations that I am creating which allows for infinite algebra.
– Shadow Sniper
Jul 30 at 21:18
If you're curious, my theory involves using transformations on equations using a new type of number that multiplies it by every possible number, creating a large set of equations from each one. Then, with all the possibilities, we scale them back down using a different method that reserves the original equation but in a different form of equations that I am creating which allows for infinite algebra.
– Shadow Sniper
Jul 30 at 21:18
So based on what you're saying, what forms of equations/functions do not allow transformations to remain the same? I am certain that most equations/functions with powers do not allow it, and also logs and possibly radicals, since they are negative powers. Would trigonometric equations preserve? Circles continue to repeat, even though they can be simplified. For example, multiplying 360 degrees by 2 is 720, but it is still geometrically 360 degrees.
– Shadow Sniper
Jul 30 at 21:26
So based on what you're saying, what forms of equations/functions do not allow transformations to remain the same? I am certain that most equations/functions with powers do not allow it, and also logs and possibly radicals, since they are negative powers. Would trigonometric equations preserve? Circles continue to repeat, even though they can be simplified. For example, multiplying 360 degrees by 2 is 720, but it is still geometrically 360 degrees.
– Shadow Sniper
Jul 30 at 21:26
Your claim is to much general in that way, maybe you could consider some concrete example to discuss here.
– gimusi
Jul 30 at 21:31
Your claim is to much general in that way, maybe you could consider some concrete example to discuss here.
– gimusi
Jul 30 at 21:31
If by concrete you mean real-life situation, I can give you one. So the amount of money John makes an hour is represented in this equation: 5x+35=67. If John's boss halved the equation, would his income in half the time be proportional? i.e., since the equation was split in half, does a value of x/2 result in a proportional answer? You can solve that, check it, blah blah. So what I'm asking is, for what types of equations or functions does that type of reasoning not remain true?
– Shadow Sniper
Jul 30 at 21:33
If by concrete you mean real-life situation, I can give you one. So the amount of money John makes an hour is represented in this equation: 5x+35=67. If John's boss halved the equation, would his income in half the time be proportional? i.e., since the equation was split in half, does a value of x/2 result in a proportional answer? You can solve that, check it, blah blah. So what I'm asking is, for what types of equations or functions does that type of reasoning not remain true?
– Shadow Sniper
Jul 30 at 21:33
 |Â
show 5 more comments
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
1
The question is really general but as a simple example if we consider $x=1$ and multiply by $x $ we obtain $x^2=x$ which is a different equation since in the latter case the solutions are $$x^2-x=0 iff x(x-1)=0 iff x=0 lor x=1$$. But it is the same equation, as it should be in a proper manipulation, if we take $xneq 0$ when multiply by $x$.
– gimusi
Jul 30 at 21:17
If you're curious, my theory involves using transformations on equations using a new type of number that multiplies it by every possible number, creating a large set of equations from each one. Then, with all the possibilities, we scale them back down using a different method that reserves the original equation but in a different form of equations that I am creating which allows for infinite algebra.
– Shadow Sniper
Jul 30 at 21:18
So based on what you're saying, what forms of equations/functions do not allow transformations to remain the same? I am certain that most equations/functions with powers do not allow it, and also logs and possibly radicals, since they are negative powers. Would trigonometric equations preserve? Circles continue to repeat, even though they can be simplified. For example, multiplying 360 degrees by 2 is 720, but it is still geometrically 360 degrees.
– Shadow Sniper
Jul 30 at 21:26
Your claim is to much general in that way, maybe you could consider some concrete example to discuss here.
– gimusi
Jul 30 at 21:31
If by concrete you mean real-life situation, I can give you one. So the amount of money John makes an hour is represented in this equation: 5x+35=67. If John's boss halved the equation, would his income in half the time be proportional? i.e., since the equation was split in half, does a value of x/2 result in a proportional answer? You can solve that, check it, blah blah. So what I'm asking is, for what types of equations or functions does that type of reasoning not remain true?
– Shadow Sniper
Jul 30 at 21:33