MHB What Does the Inequality x >= y Mean?

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The inequality x >= y indicates that for any values of x and y, x is always greater than or equal to y. This means that no matter what specific values are chosen for x and y, the relationship will always hold true. The discussion emphasizes the universality of this inequality across all possible pairs of x and y. Understanding this concept is crucial for interpreting mathematical relationships and functions. The principle underscores foundational aspects of inequality in mathematics.
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∀x∀y (x >= y)
 
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WannaBe said:
∀x∀y (x >= y)

For all $x$ and for all $y,$ $x$ is greater or equal than $y.$
 
For any pair $$(x,y)$$ the inequality $$x\geq y$$ holds.
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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