Please correct me if I’m wrong, but x isn’t specifically part of the sequence a-z, right? And a-z isn’t explicitly a consecutive sequence. Both are implied, but they’re all just placeholders for individual numbers, not necessarily in relation to each other.
If that is the intention, it’s poorly done. (1-x)(2-x)(3-x)…(∞-x) is much clearer and understandable.
I think it’s correct as is. The “…” is used when enough information is present to complete the series.
For example, if the series really is anything other than the alphabet as it is commonly understood, (thus excluding “x”,) then that would need to be made clear by the person communicating the series.
For example, we can say with confidence that your example, “1, 2, 3…∞” is indeed the set of natural numbers, including “24” if we were to write them all out.
they’re all just placeholders for individual numbers
Just normal variables, although used in a kinda “gotcha” way by obfuscating the “number minus itself” trick. There’s a very common teacher’s trick that relies on the same principle. You balance a certain equation and “prove” on the blackboard that 0=1. It’s incumbent on the students, then, to figure out that halfway through your shenanigans, you divided the right half of the equation by “x-x”. This is dividing by zero, which is impossible, and thus explains your farce.
Correct. Let a-z be the first 26 prime numbers and x be an unknown real number, for example. It cannot be categorically stated in this case that it simplifies to zero.
Not correct. The variable “x” cannot represent both the 24th prime number as well as an unknown real number. If you wanted to represent your proposition it would need to be written differently than in the meme
But the problem with the meme is orecisely the ambiguity of whether or not x belongs to the set {a, b, c,…,z} due to x’s universal use as “the” variable.
It is not ambiguous. The set {a, b, c,…z} contains every letter. “x” being a popular choice to use as a variable in general does not confer to it any other special significance that would exclude it from the set of alphabetically arranged letters
You are indeed a math person!
Please correct me if I’m wrong, but x isn’t specifically part of the sequence a-z, right? And a-z isn’t explicitly a consecutive sequence. Both are implied, but they’re all just placeholders for individual numbers, not necessarily in relation to each other.
If that is the intention, it’s poorly done. (1-x)(2-x)(3-x)…(∞-x) is much clearer and understandable.
You could argue it’s implied that a-z sequence contains x. But I agree that it’s a bit ambiguous.
Here’s what a better notation would look like:
Or
This way, both Bn and X could be any number and not just natural ones.
I think it’s correct as is. The “…” is used when enough information is present to complete the series.
For example, if the series really is anything other than the alphabet as it is commonly understood, (thus excluding “x”,) then that would need to be made clear by the person communicating the series.
For example, we can say with confidence that your example, “1, 2, 3…∞” is indeed the set of natural numbers, including “24” if we were to write them all out.
Just normal variables, although used in a kinda “gotcha” way by obfuscating the “number minus itself” trick. There’s a very common teacher’s trick that relies on the same principle. You balance a certain equation and “prove” on the blackboard that 0=1. It’s incumbent on the students, then, to figure out that halfway through your shenanigans, you divided the right half of the equation by “x-x”. This is dividing by zero, which is impossible, and thus explains your farce.
Correct. Let a-z be the first 26 prime numbers and x be an unknown real number, for example. It cannot be categorically stated in this case that it simplifies to zero.
Not correct. The variable “x” cannot represent both the 24th prime number as well as an unknown real number. If you wanted to represent your proposition it would need to be written differently than in the meme
But the problem with the meme is orecisely the ambiguity of whether or not x belongs to the set {a, b, c,…,z} due to x’s universal use as “the” variable.
It is not ambiguous. The set {a, b, c,…z} contains every letter. “x” being a popular choice to use as a variable in general does not confer to it any other special significance that would exclude it from the set of alphabetically arranged letters