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James_fl
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Well obviously, no is the answer. But why?
After all: If 5! = x! then x = 5.
After all: If 5! = x! then x = 5.
James_fl said:No, because the 5 in f(x) = 5 is a constant.
Couldn't you also by inspection say that if x!=1! that x is either 1 or 0?James_fl said:matt grime: if factorial function is not injective, then why is it that i can show by inspection: if 5! = x!, then x=5? My Math knowledge is limit, so my apology if I am mistaken, but surely, there is no other value that can satisfy x except 5?
Because it happens to work for 5 (and many other numbers ), but not in general, so not always.James_fl said:matt grime: if factorial function is not injective, then why is it that i can show by inspection: if 5! = x!, then x=5? My Math knowledge is limit, so my apology if I am mistaken, but surely, there is no other value that can satisfy x except 5?
matt grime said:It so happens that the factorial function is not injective.
It can't, it's either injective or notJames_fl said:dav2008: yes, i could, which means the factorial function is also not injective. But how could a function be injective (assuming my argument is true) and not injective at the same time?
James_fl said:dav2008: yes, i could, which means the factorial function is also not injective. But how could a function be injective (assuming my argument is true) and not injective at the same time?
dav2008 said:Who is saying that it's injective?
James_fl said:matt grime: if factorial function is not injective, then why is it that i can show by inspection: if 5! = x!,
Why should it work? It simply doesn't because it doesn't follow from the definition of the factorial.James_fl said:TD: Yes, it doesn't work for 1!, but why? I'm confused :(
James_fl said:I think I need to clarify. I don't know if it is injective or not, but if it is not injective, and I'm sorry to repeat this, why if 5! = x! then x=5?
While it TD is right in saying that it wouldn't work for some numbers, I still don't get it. Possibly, there is some circular logic in my argument. I'm not sure...
Correct.James_fl said:I understand to prove a statement, I need to prove it for a general case. So in that sense, 5! = x! means x=5 does not constitute as a proof as it only works for this case.
Not because it can't be proven, it can even be disproven: 0! = 1! but 0 =/= 1.James_fl said:So, can I just say that since it can't be proven that x! is a one-to-one function, the statement x!=y! does not imply that x = y?
James_fl said:matt grime: No need to be hostile, I am just a high school student looking to understand a concept. Maybe "argument" is not the correct word since it is only my assumption. I understand to prove a statement, I need to prove it for a general case. So in that sense, 5! = x! means x=5 does not constitute as a proof as it only works for this case.
So, can I just say that since it can't be proven that x! is a one-to-one function
the statement x!=y! does not imply that x = y?
That depends on your definition of n!James_fl said:whoa a lot of replies.. so the n! function is injective for all values of n except 0 and 1, right?
matt grime said:To prove something 'for all' whatever you cannot just use one example. However to demonstrate that a statement of 'for all' is false it suffices to find a single counter example (like 0!=1! here). You've just learned the first lesson in what it takes to prove or disprove something.
This statement is a mathematical contradiction, as 0 and 1 are two different numbers with distinct values. Therefore, it is not logically possible for 0 to equal 1.
Even if we redefine the values of 0 and 1, we would still have two distinct values, making it impossible for 0 to equal 1. The concept of equality is based on the idea that two things must have the same value or quantity in order to be considered equal.
No, it is not possible to manipulate the equation to make 0 equal 1. This is because the equation is based on the fundamental properties of numbers and their operations, which cannot be altered.
No, this statement is purely a mathematical concept and has no relation to any scientific theories or phenomena. It is simply a logical contradiction in the world of mathematics.
This statement has no significance in mathematics as it contradicts the fundamental concepts of numbers and their operations. It is considered a nonsensical statement and holds no value in mathematical theory or practice.