Hi everyone,

Your midsemester grades, which include the grades for Exam #2, are now posted on the Grades page. Let me know if you have any questions, and send me an email if you have forgotten the password to the Grades page.

Regards,

Prof. Reitz

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Hi everyone,

Your midsemester grades, which include the grades for Exam #2, are now posted on the Grades page. Let me know if you have any questions, and send me an email if you have forgotten the password to the Grades page.

Regards,

Prof. Reitz

- Combinatorics - 2023 students who belong to either one of two categories February 5, 2023Suppose we have 2023 students. Each student can either be lying or telling the truth. We know that each student knows which category (lying or telling the truth) they belong to, and that each student knows what category the other students belong to. We also know that all 2023 students can be put in a […]john doe
- Negating "There is some $\epsilon>0$ such that $f(x)>0~$ for all $x>0$" February 5, 2023I have to make the negation of the following sentence. There is some $\epsilon>0$ such that $f(x)>\epsilon~$ for all $x>0$. Here is my attempt: For each $\epsilon>0$, $f(x)\leq \epsilon~$ for some $x>0$. Am I correct?LoveMath
- How do I symbolically express a statement of the form "Something, given that something is true, will be something"? February 5, 2023I am focusing especially on the "something, given that something is true" part. An example would be "An equation in the form $ax^2$ given that $a \ne 0$ will have a derivative greater than $0$." Instead of saying "$ax^2$ given that $a \ne 0$", can I instead say one of the below? "$ax^2$ | $a […]Peashooter8890
- Which of these is the correct way of saying "given that"? [duplicate] February 5, 2023For example, I want to say "Given that $\alpha$ is not infinity, $\alpha$ is not infinity. (Stupid example but just an example)" Which of these is the correct way of saying it? $\alpha \ne \infty | \alpha \ne \infty$ $\alpha \ne \infty : \alpha \ne \infty$ $(\alpha \ni (\alpha \ne \infty)) \ne \infty$ Given that […]Peashooter8890
- Is $\forall x (\phi)$ a formula in ZF even if $\phi$ does not contain x? February 5, 2023I was reading A Quick Introduction To Basic Set Theory by Anush Tserunyan, and in definition 1.1, the author defined a notation of a formula in ZF with few criterias. One of them states: If $\phi$ is a formula and $x$ is a variable, then $\forall x(\phi)$ and $\exists x(\phi)$ are formulas. I remember in […]wsz_fantasy
- Rewriting $((P→Q)∨(P∧Q))↔¬(P∨Q)$ using just Not, And, Or February 4, 2023I have a simple formula that I would like to write only using negation, alternative and conjunction, getting rid of the equivalence $↔:$ $$((P→Q)∨(P∧Q))↔¬(P∨Q)$$Abradab3
- Do incompleteness theorems require circular referencing? February 4, 2023Across many fields of math, and related fields like logic and computer science, there are incompleteness theorems that state a system cannot be both consistent and complete. Some examples include (simplifying a lot): Gödel incompleteness theorem: "The i-th statement cannot be proved", where the i-th statement is that text. Logical statement: "This sentence is false" […]Aaron Franke
- Is there a scenario for when changing the order of different quantifiers in a nested quantifier retain the original meaning? February 4, 2023I was exploring the difference in meaning of a proposition when changing the order of two different quantifiers in a nested quantifier. I've been sitting here playing around with various scenarios and doing a bit of research, but I'm unable to come to a decisive answer. Does changing the order of different quantifiers always change […]apill4
- How does one prove there exists an object with some property? [closed] February 4, 2023One of the things that I always considered very difficult in math is proving that a certain object exists. Suppose we want to prove that an object $a$ with the property $p$ exists. There are two main approaches, the first is to explicitly construct the object and although far for trivial, at least we know […]NickThom
- Correspondence between inductively definable and countable February 4, 2023Working within ZFC: Is the collection of all countable sets (call it $C$) a well-defined set, or is it a proper class? If $C$ is a set, I would suspect it's at least uncountable. For example the elements of $P(\mathbb{N})$, the power set of $\mathbb{N}$, are countable and hence are elements of $C$ (i.e. $P(\mathbb{N})\subseteq […]John Smith

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