Question Number 62399 by naka3546 last updated on 20/Jun/19
$${What}\:\:{the}\:\:{definition}\:\:{of}\:\:{Claim}\:,\:{Theorem}\:,\:\:{and}\:\:{Lemma}\:\:? \\ $$$${When}\:\:{can}\:\:{we}\:\:{use}\:\:{them}\:\:{respectively}\:\:{for}\:\:{getting}\:\:{proof}\left({s}\right)\:? \\ $$
Answered by alphaprime last updated on 20/Jun/19
$${Lemma}\:−\:{A}\:{proven}\:{statement}\:{used}\:{for}\: \\ $$$${proving}\:{another}\:{statement}\:.\:{It}\:{maybe}\:{like} \\ $$$${any}\:{general}\:{hypothesis}\:{you}'{ve}\:{proven}\:{through} \\ $$$${mathematical}\:{induction}. \\ $$$${Theorem}\:{is}\:{mathematical}\:{statement}\:{always} \\ $$$${true}\:{and}\:{used}\:{to}\:{deduce}\:{or}\:{generate}\:{other}\:{higher}\:{profiles} \\ $$$${in}\:{maths}\:,\:{it}'{s}\:{pure}\:{and}\:{not}\:{considered}\:{in}\:{applied} \\ $$$${mathematics}\:. \\ $$$${Claim}\:{can}\:{be}\:{any}\:{proposition}\:{which}\:{you}\: \\ $$$${believe}\:{to}\:{be}\:{either}\:{true}\:{for}\:{further}\:{proceedings} \\ $$$${in}\:{maths}\:{or}\:{ain}'{t}\:{sure}\:{about}\:{it}\:,\:{which}\: \\ $$$${later}\:{can}\:{be}\:{evaluated}\:{by}\:{many}\:{methods}\: \\ $$$${or}\:{alhorithms}. \\ $$$${Well}\:{you}\:{gotta}\:{join}\:{my}\:{workspace}\:{for}\:{knowing}\: \\ $$$${about}\:{construction}\:{of}\:{proofs}\:{and}\:{everything}\: \\ $$$${about}\:{it}.\: \\ $$