{{m, x)| m is a turing machine that runs on input x for an even let even number of steps}. of course, a turing machine running for infinitely many steps neither runs for an odd nor an even number of steps. we want to show that even is undecidable by a proof from scratch (i. e., by diagonalization not by a reduction) first we assume even is decidable, i. e., there is a tm h that accepts (m, x) if m is a turing machine that runs on input x for an even number of steps, and rejects otherwise. we want to do the diagonalization in two stages. (a) first, describe a tm d (based on the supposedly existing tm h) accepting (m) if and only if m is a turing machine that runs on input (m) for an even number of steps. otherwise d rejects note that you may assume the correctness of the church-turing thesis, i. e., instead of describing a turing machine in detail, you can just describe an algorithm in pseudo-code. (b) now define a tm d from d that runs on (m) for an odd number of steps if d accepts (m). otherwise d runs for an even number of steps (c) how does the existence of this produce a contradiction? (d) what does the contradiction prove?

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a macro is a tool that allows you to automate tasks and add functionality to your forms, reports, and controls. for example, if you add a command button to a form, you associate the button's onclick event to a macro, and the macro contains the commands that you want the button to perform each time it is clicked.

we can all learn from our past mistakes because we all have different ways of learning different types of techniques. my way may or may not another classmate remember and have the repetition to acknowledge such standard. such as remembering acronyms. using abbreviations to us remember keep things in order in our memory. this us figure out what comes next in the sequence. if so, what we have is a sentence of just letters all in caps. we either know the meaning or have no idea what it stands for. most of the time we know the meaning and context. but most of us who don't know, should learn by having a quick glance at what needs to be remembered. such as repetition in the memory for acronyms. one way that me, is the fact that i'm always doing math and english assignments. so we have to remember specific meanings such as soapstone for documents, such as citing correctly. or pemdas for doing the equations correctly, even if it's the super long way. this works for everyone. you just have to find what works for you by practicing and repetition daily.