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Couperin
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It's a word I hear a lot and I've looked it up but I don't understand. What does it mean to be rigorous in one's mathematics?
Rigorous doesn't mean difficult...symbolipoint said:eyehategod in message #4 was close. Rigorous is difficult, stressing critical thinking in learning and applying fundamental notions. (Or substitute properties, knowledge, concepts, and skills, instead of "notions".)
ice109 said:all you people need a dictionary. rigorous doesn't mean hard. arduous means hard
ice109 said:it means that all of your conclusions are deduced using proper mathematical rules.
for example
[tex]5x^2=x[/tex]
[tex]x=1/5[/tex] only if [tex] x \neq 0[/tex]
because in deriving that conclusion you divided by x and x can't be zero because you can't divide by zero.
DeadWolfe said:Rigorous means, precise, no steps left out, no assumptions left unstated
not definitions vague, etc...
Rigor in science refers to the strict adherence to a set of procedures, guidelines, and standards in conducting research, experiments, or investigations. It involves a high level of precision, accuracy, and attention to detail to ensure the validity and reliability of scientific findings.
While rigor refers to the strict adherence to procedures and standards, accuracy refers to how close a measurement or observation is to the true value, and precision refers to the consistency and reproducibility of measurements or observations. Therefore, rigor is necessary for ensuring the accuracy and precision of scientific findings.
Rigor is crucial in science because it ensures that research and experiments are conducted in a systematic and unbiased manner. This allows for the replication and verification of results, leading to the advancement of scientific knowledge and the development of new theories and technologies.
To ensure rigor in scientific work, one must carefully plan and follow a detailed methodology, accurately record and analyze data, critically evaluate results, and communicate findings with transparency and honesty. Peer review and replication of experiments also contribute to ensuring rigor in scientific work.
Lacking rigor in scientific research can lead to inaccurate and unreliable results, which can have serious consequences in various fields such as medicine, engineering, and environmental science. It can also damage the credibility of the scientific community and hinder the progress of scientific knowledge.