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I'm trying to express the following sentence:

"A condition is true when $X$ is greater than or equal to any value of $X_m$, where $m$ consists of $1,2,...$." (note: where $m$ stops is not known in advance)

I've currently got that sentence expressed mathematically as,

$X \ge X_m \; ; \; m = 1,2... $

What would be the best way to prevent that math expression from being misinterpreted as as "...$X$ is greater than or equal to all values of $X_m$..."?

plu
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  • What you call "expressed mathematically" is neither a formula (expression) nor a phrase (sentence). It has neither the precision of formal language nor the accessibility of natural language, but combines the worst of two worlds. – Marc van Leeuwen Jul 30 '19 at 21:42
  • @MarcvanLeeuwen Isn't that the point of the question? – Théophile Jul 30 '19 at 21:45
  • @Théophile In a sense you are right. But OP presents this a bit like: "I've come so far but how do I proceed?", while as my comment points out this is already off the track, the "expression" is broken, and it is not a matter of proceeding but of starting over with a better idea of what the task is really about. – Marc van Leeuwen Jul 31 '19 at 06:47
  • @MarcvanLeeuwen I was just trying to express the original sentence accurately and succinctly, which Theophile's had provided a satisfactory answer for. For application-related reasons I'm stuck with using $X$ and $X_m$; I didn't reveal what this task was really about (the full context, many more terms involved) because it would be off-topic for this SE. – plu Jul 31 '19 at 21:48

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How about: $$\exists m\ge1 : X \ge X_m,$$ in other words, "There exists an $m \ge 1$ such that $X \ge X_m$."

Théophile
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