The Topic:
Final number?

The Question:

No, it's zero! After all, 3.1416 = 3.1416000000000000...

I mean, yeah, chaos theory isn't REAL mathematics, but you'd think he'd know THAT at least.

Regis Philbin  

Is that your final number?

 Ian Malcolm

Actually, 3.1416 is not the same as 3.14160000... as the second number implies a degree of certainty which is not implicit with the first number. Also, even if two numbers are equal, it does not mean that they are the same number. A subtle distinction to be sure, but it nonetheless proves me correct.

 Ian Malcolm

Oh, and can we please get Regis to shut up?


Look, punk, we're talking "pure mathematics" here. The actual numbers are equivalent, assuming we're speaking decimal here. The use of trailing zeros does indeed imply confidence in the measurement technique used to acquire the extra zeros, but that does not affect the actual number.

Equality is by definition a reflexive, symmetric, and transitive relation on the set under consideration, in this case the set C of all complex numbers and its subset R, consisting of all real numbers.

Go up to any grade-school, high school, or college mathematics professor/teacher and ask him/her to verify that 3.14160 = 3.1416. This will establish the initial hypothesis. Now, by the definition of symmetry on a set relation, we can "reverse" the statement, showing that 3.1416 = 3.14160.

Oh, and I'll help you take Regis down if you can prove that all even integers > 2 are expressible as the sum of two prime integers.

 Ian Malcolm

Okay, listen up, Psilon boy, while I lay some logical smack down. It's like this. The name "Richard" is "equal" to the name "Dick" because they both mean the same person. But if you try to tell me that the last letter in Richard is "k" you're just plain wrong. It doesn't matter that you're also a Dick.

 Ian Malcolm

Anyway, I'm the one wearing cool sunglasses here, and I think that ends the argument.

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