From 5b11d9202a0c3cc7609feff20113477c258d6557 Mon Sep 17 00:00:00 2001 From: Philippe Zwietering Date: Tue, 16 May 2023 15:48:46 +0200 Subject: [PATCH] Changed my commentary on failure to be cursive --- assignments/week1/1.pdf | Bin 481922 -> 487434 bytes assignments/week1/1.tex | 5 +++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/assignments/week1/1.pdf b/assignments/week1/1.pdf index 33735dc99ee2082e876f23738c9d71f3adcf5d29..257c4416d610766b77d92df35e90b6dfdb6bc826 100644 GIT binary patch delta 98669 zcmV(zK<2-KwH=D!9kAyz0y8<65FiIAf8AVJkKDKse)q5Fw`c+nm-peod01c*I6xLy ztb;tn2_jGTc(l`p-N%k6zdpr72iero$J$O{z@wHZs#xb&B#U_VVTNaaeu2Z^@87=o z?oZsz2th^&I(vIRqnILQ^h_~=1mm-}^VvU&k2n8(`xn+f7mtJ zhDH)@8l|M`4RIr8w*(RR<64oXRom4qMVifSB~rvht$?HsX$DbAp-V}mZ}kon-cZ(Q zC=lTc2Kc3Dr{-MZZz-keRc1g$plJhQM#Td%(SR7$en5eSA2VIq0ck$FRfsSeHH!xX zmrM)j)G%@-ag0)Lrcp0))PvNzf7DZiBjR6Y`A!g)x+eWo=6eDu9BI-nt4WIJaZO@~ zDKSNpG}b4ZK_BsK3i0YUCjJ~V7?MV#NV~iuX&EWfUvrAY5Vy@biuBj48GxIhY^oXX 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I see that this is definitely injective, since the way the exponents + \textit{I'm kinda stuck at this point. + I see that this is definitely injective, since the way the exponents are defined, you will always know which prime factors belong to the numerator or to the denominator. But I fail to prove this using the direct definition of $f$ like we could do for the natural numbers. This is because the products of the denominators in the last equation are not unique. So maybe I simplified them too much and shouldn't try and write them in terms of $x_1$ and $x_2$ like we did earlier, and try and focus more on just the exponents, but I feel it becomes really hard - to show that $x_1 = x_2$ that way. + to show that $x_1 = x_2$ that way.} \item[Surjectivity:] We want to show that $f$ is onto, i.e. $f(\{ q > 0 : q \in \Q \}) = \N$.