1/9/2023 0 Comments Stronger definitionSo I was looking to understand a better way to understand what a stronger statement means without "cheating".Īs pointed out by the comment, A is stronger because it says everything B says and more. its not a proof nor I expect it to be the "real reason" why the definition holds. So I assume its a fine memory device but its oversimplifing things "cheating" in some way. The only issue I have with my memory device is that I obviously just re-define what the statement A means to be a very specific set membership statement. Furthermore, if x is in B it doesn't necessarily always be in A, so the converse is not always true automatically. Therefore, being in A implies being in B. ![]() I draw the following diagram:Īnd then notice that whenever x is in A it means it must be is B also. In fact I create some type of "memory device" (not sure what else to call it) to remember/justify it to myself. Is a stronger statement than B B is weaker than A.Īnd I was wondering, why is the definition that way? Is there a conceptual/intuitive way to explain this? I know this is just "the definition" but I was trying to understand why it is that way. If $A \implies B$ is true, but $B \implies A$ is false, we say: A ![]() ![]() ![]() I came across the following definition (from Mattuck's Analysis book): I was trying to understand the meaning or the definition of what a "stronger statement" is formally.
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