What information do you get out of 1=1? You can pull out that there is an identity element, where 1 denotes a multiplicative element. Anything else? maybe... but not much.ghostmonkey said:Is every conceivable equation not simply a circular representation of 1? If F=ma, then F=F and 1=1. If a=a, then 1=a/a=1. If E=MC^2, then E=E=1=1. How is mathematics an infallible language then? We should ultimately be able to conjure up even the most complex of equations, all being equatable to 1.
No, because in going from F= ma, to F= F you are dropping information. I could as easily say that F= ma2 and derive F= F from that, even though F= ma2 is untrue. I note you say "We should ultimately be able to conjure up even the most complex of equations, all being equatable to 1" but every example you give goes the other way. It's easy to lose information. The hard part is gaining it. If I am given 2 and 3 I can say, without question, that 2+ 3= 5. But that does not help me solve the problem "if x+ y= 5 what are x and y".ghostmonkey said:Is every conceivable equation not simply a circular representation of 1? If F=ma, then F=F and 1=1. If a=a, then 1=a/a=1. If E=MC^2, then E=E=1=1. How is mathematics an infallible language then? We should ultimately be able to conjure up even the most complex of equations, all being equatable to 1.
ghostmonkey said:What information is there to be gotten out of 1=1? Probably nothing, if you're looking for differentiation.
ghostmonkey said:Otherwise, maybe 1=1 gives us the fundamental state of the universe, which is to also say that 0=1-1
loseyourname said:ghostmonkey, I hate to do this to you, rather than straightforwardly answer the question myself, but you will understand the difficulty you are having much better after reading Frege's On Sense and Reference.
Absolutely not! The first statement tells me how x and y are related; neither of the latter statements does.ghostmonkey said:But, regarding the x+y=5 equation, the trouble that I have is that if the sum of x and y is equal to 5, then (x+y) and 5 are identical statements, which is to say that (x+y)=(x+y) and 5=5, or 1=1.
No, they are terms (or quantities, if you like); they are not statements.then (x+y) and 5 are identical statements
When we say 1 = 1 = 1, it means that three different values (1, 1, and 1) are all equal to each other. In other words, they have the same numerical value.
1 can equal 1 in two different ways: as a mathematical expression or as a logical statement. In mathematics, 1 = 1 is a basic principle of equality, meaning that any number is equal to itself. In logic, 1 = 1 is a tautology, meaning that it is always true regardless of the values of the variables involved.
The statement 1 = 1 = 1 may have a deeper meaning in different contexts. In mathematics, it can be seen as a basic principle of equality and a starting point for more complex equations. In philosophy, it can be interpreted as a statement about the nature of identity and the concept of oneness.
No, 1 = 1 = 1 is always true and cannot be false. As mentioned earlier, it is a tautology, meaning that it is always true regardless of the values involved. In mathematics, false statements are those that contradict known facts or violate logical rules, and 1 = 1 = 1 does not fall into either category.
In scientific research, 1 = 1 = 1 can be used as a guiding principle to ensure consistency and accuracy in measurements and data analysis. It also highlights the importance of reproducibility, where the same results should be obtained when an experiment is repeated. Additionally, the statement can be applied in statistical analysis to determine if two or more groups are significantly different from each other.