how do you finish off your proofs? (1 Viewer)

[f7eeting]

me personally, i like to use QED

 

[Average Boreduser]

quod erat demonstrandum

 

[f7eeting]

quod erat demonstrandum

you write the whole thing out? seems i need to step up my game

 

[hsc_resources]

I do #QED.

 

[coolcat6778]

"question done", which is the same as QED

 

[WeiWeiMan]

me personally, i like to use QED

when using latex, quod erat demostrandum in full
on paper, QED

 

[Flatuitous]

me personally, i like to use QED

In conclusion, having meticulously established the base case and subsequently demonstrated that if the statement holds true for an arbitrary positive integer k, it must also hold for k + 1, we have effectively validated our original assertion through the rigorous framework of mathematical induction. This method not only showcases the power of logical reasoning in mathematics but also illustrates the iterative nature of mathematical truths, where the validity of one case inherently supports the next. By confirming the base case, we initiate a domino effect, establishing a foundation upon which all subsequent cases can rely. The transition from k to k + 1 is not merely a step but a critical link that fortifies the entire structure of our proof, allowing us to generalise our findings across all positive integers. Thus, we assert with confidence that the proposition holds for all integers n ≥ 1, reinforcing the elegance and interconnectedness of mathematical concepts. This proof not only serves as a testament to the specific statement under consideration but also exemplifies the broader principles of deductive reasoning and the profound implications of induction in mathematical theory. Therefore, we conclude that the statement in question is indeed true for all positive integers, reflecting the beauty and consistency inherent in the realm of mathematics, where each proven statement builds upon the last, weaving a tapestry of knowledge that spans the infinite landscape of numerical exploration.

 

[f7eeting]

In conclusion, having meticulously established the base case and subsequently demonstrated that if the statement holds true for an arbitrary positive integer k, it must also hold for k + 1, we have effectively validated our original assertion through the rigorous framework of mathematical induction. This method not only showcases the power of logical reasoning in mathematics but also illustrates the iterative nature of mathematical truths, where the validity of one case inherently supports the next. By confirming the base case, we initiate a domino effect, establishing a foundation upon which all subsequent cases can rely. The transition from k to k + 1 is not merely a step but a critical link that fortifies the entire structure of our proof, allowing us to generalise our findings across all positive integers. Thus, we assert with confidence that the proposition holds for all integers n ≥ 1, reinforcing the elegance and interconnectedness of mathematical concepts. This proof not only serves as a testament to the specific statement under consideration but also exemplifies the broader principles of deductive reasoning and the profound implications of induction in mathematical theory. Therefore, we conclude that the statement in question is indeed true for all positive integers, reflecting the beauty and consistency inherent in the realm of mathematics, where each proven statement builds upon the last, weaving a tapestry of knowledge that spans the infinite landscape of numerical exploration.

very short, straight to the point, no waffle at all. will definitely be using this the next time i do induction