How did they find out how to do it the correct way? I mean sometimes when i do a problem wrong, it still gives me an answer and i can continue calculating with that answer, so if i was a mathematician how would i know that is wrong? Does my wrong answer stop somewhere and gets impossible to calculate?
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The higher up in math you go, the more organized your calculations are.
As you note each operation you do, you will eventually be able to find mistakes that you make when either checking your work or reviewing it.
As you note each operation you do, you will eventually be able to find mistakes that you make when either checking your work or reviewing it.
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Logic.
We can look at something like 2+2=4. We can verify it millions of times over, and it will never equal something that isn't 4.
Any calculation you could ever devise will have an answer, have thing like sqrt-1 or x/0.
We can assume that for general algorithms there may have been hundreds and hundreds of trials to ensure that said algorithm is sound and will always work.
But yeah. If you think about any equation logically, you'll be able to find an equation.
Except for calculus. That **** it whack.
We can look at something like 2+2=4. We can verify it millions of times over, and it will never equal something that isn't 4.
Any calculation you could ever devise will have an answer, have thing like sqrt-1 or x/0.
We can assume that for general algorithms there may have been hundreds and hundreds of trials to ensure that said algorithm is sound and will always work.
But yeah. If you think about any equation logically, you'll be able to find an equation.
Except for calculus. That **** it whack.
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There's usually a way to check your answer. If you're solving an equation for x, you can put that x back into the equation and see if it works. You should get into the habit of doing this on tests.