# Tagged Questions

For questions about the formulation of a proof, not about the mathematics behind it.

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### Subset relation ⊆ on all subsets of ℤ is a partial order, not a total order.

I need to prove that the subset relation “⊆” on all subsets of ℤ is a partial order but not a total order. I'm not experienced in these kind of proofs and was hoping to see an example of an easier one ...
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### Proof for length of graph

G is a simple graph that consists of a vertex set V(G) = {v1, v2, ..., vn} and an edge set E(G) = {e1, e2, ..., em} where each edge is an ordered pair of vertices. The edge {u,v} is denoted uv. A ...
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### Proof for Theorem of Upper and Lower Bounds On Zeroes of Polynomials

I'm currently a high school Pre-Calculus student and my textbook presents the following theorem without proof: Let $f(x)$ be a polynomial with real coefficients and a positive leading coefficient. ...
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### Is there any way to gain some insight into a proof by simply looking at a graphic?

My school is using Pinter's "A Book of Abstract Algebra" for both semesters of Modern Algebra. For a class assignment a couple weeks ago, regarding rings, I was tasked with the following problem ...
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### How to minimize $ab + bc + ca$ given $a^2 + b^2 + c^2 = 1$?

The question is to prove that $ab + bc + ca$ lies in between $-1$ and $1$, given that $a^2 + b^2 + c^2 = 1$. I could prove the maxima by the following approach. I changed the coordinates to spherical ...
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### Prove or disprove these statements. [closed]

I have this statement and I need to prove or disprove it. Any help is appreciated. (1) Is it possible for solution set of a system [A| $\vec{b}^.$] of three equations and three variables, and ...
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### Proving by induction that a balanced strings of parentheses has equally many opening and closing parentheses

In computer science, a string is a finite sequence of characters. For strings $A$ and $B$, we express $AB$ as $A$ followed by $B$. A balanced string of parentheses is a string of open and closed ...
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### Prove the following simple exponentiation equality.

Having trouble with the following proof. Given $b > 1, c > 0$, prove that $\exists \; x$ s.t. $b^{x} < c$. We can't use $log$, and I have already shown that $b^{x} > c$ by using the ...
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### Theorem 2.27 (a) in Baby Rudin: Is his proof complete enough?

Here's Theorem 2.27 (a) in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition: If $X$ is a metric space and $E \subset X$, then $\overline{E}$ is closed. Now here's ...
### Prove $\log(x)^{10} < x$ (for $x > 10^{10}$)
I need to prove that $\log(x)^{10} < x$ for $\ x>10^{10}$ It's pretty clearly true to me, but I need a good proof of it. I tried induction, and got stuck there.