Equation VS formula
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marmoset
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I couldn't think of the answer, but I found this: S.O.S. Mathematics CyberBoard :: View topic - Formula vs. Equation
And I came to the conclusion that an equation has an equal sign. We often see formulas expressed with an equal sign, but the formula is actually the rule for figuring something out. So when the area of a circle (A) = pi r squared (sorry, I don't know how to properly insert pi and squared), the "pi r squared" is the formula. I think.
I couldn't think of the answer, but I found this: S.O.S. Mathematics CyberBoard :: View topic - Formula vs. Equation
And I came to the conclusion that an equation has an equal sign. We often see formulas expressed with an equal sign, but the formula is actually the rule for figuring something out. So when the area of a circle (A) = pi r squared (sorry, I don't know how to properly insert pi and squared), the "pi r squared" is the formula. I think.
birdeen's call
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An equation must have the equality sign, but it's not enough to make a formula an equation. An equation needs unknown variables (which don't have to be written down).
x+3=5
x+y=z
The above are equations. We may think of them as questions. The question is, "What are the possible values of the variables?"
Another kind of formula that has an equality sign is an equality. An equality is not a question; it's an assertion. When I say
2=2,
I'm giving you an equality. I'm not asking you anything. I'm just saying that two equals two. I could say
2=3
too. This is also an equality if I'm asserting this, although it's a false one.
I can think of 2=2 as an equation too. I could ask, "If 2=2, then what can be the value of x?" Of course, the answer is "any value". "2=2" is always true, so whatever value we assign to x, it doesn't stop being true. Similarly, if I asked what the possible values of x are in 2=3, the answer would be "no values". It's always false, and it doesn't matter what value x has. Thus, the equation 2=3 has no solutions.
I can think of x+3=5 as an equality too. I might not know the x, but know that x+3=5. Then I could assert it and say "x+3=5". If I'm not asking what the possible values of x are, then I'm just giving you an equality, not an equation.
The above is just a popular explanation. It's not a logician's one, because it would require some difficult words. It could also differ from what I've just written.
A formula is any string of mathematical (or other scientific) symbols. The word has several meanings.
x+3=5
x+y=z
The above are equations. We may think of them as questions. The question is, "What are the possible values of the variables?"
Another kind of formula that has an equality sign is an equality. An equality is not a question; it's an assertion. When I say
2=2,
I'm giving you an equality. I'm not asking you anything. I'm just saying that two equals two. I could say
2=3
too. This is also an equality if I'm asserting this, although it's a false one.
I can think of 2=2 as an equation too. I could ask, "If 2=2, then what can be the value of x?" Of course, the answer is "any value". "2=2" is always true, so whatever value we assign to x, it doesn't stop being true. Similarly, if I asked what the possible values of x are in 2=3, the answer would be "no values". It's always false, and it doesn't matter what value x has. Thus, the equation 2=3 has no solutions.
I can think of x+3=5 as an equality too. I might not know the x, but know that x+3=5. Then I could assert it and say "x+3=5". If I'm not asking what the possible values of x are, then I'm just giving you an equality, not an equation.
The above is just a popular explanation. It's not a logician's one, because it would require some difficult words. It could also differ from what I've just written.
A formula is any string of mathematical (or other scientific) symbols. The word has several meanings.
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