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buzzee
  • Member for 8 years, 6 months
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17 votes
7 answers
107k views

Example of a relation that is symmetric and transitive, but not reflexive [duplicate]

8 votes
5 answers
20k views

Example of a relation that is reflexive but not symmetric [duplicate]

8 votes
1 answer
21k views

Is there no difference between upper triangular matrix and echelon matrix(row echelon matrix)?

7 votes
1 answer
6k views

Why zero is a multiple of every integer, but not a divisor of zero?

7 votes
2 answers
3k views

Anybody knows a proof of Uniqueness of the Reduced Echelon Form Theorem?

6 votes
4 answers
22k views

Proof of $n(n^2+5)$ is divisible by 6 for all integer $n \ge 1$ by mathematical induction

5 votes
4 answers
4k views

What's the benefit of using strong induction when it's replaceable by weak induction?

4 votes
1 answer
29k views

Is it okay to determine pivot positions in a matrix in echelon form, not in reduced echelon form?

4 votes
2 answers
985 views

Why is {1, 2, 3} an equivalence relation?

3 votes
1 answer
2k views

What is the probability that if n =39 a randomly chosen array element is in A[$\lfloor n/2 \rfloor$], A[$\lfloor n/2 \rfloor$ + 1], . . . , A[n]?

3 votes
4 answers
440 views

Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$ [duplicate]

3 votes
3 answers
740 views

Proof of for all integer $n \ge 2$, $n^3-n$ is divisible by 6 by mathematical induction.

2 votes
4 answers
69 views

How is $\Bbb Z_0 = \{0, \pm m, \pm2m, \pm3m, \ldots\}$ denoted in set builder notation?

2 votes
4 answers
4k views

Using a truth table to show that an argument form $(p\rightarrow q) \land q \rightarrow p$ is invalid.

2 votes
2 answers
833 views

Is it correct to say gcd$(r, 0)$? The definition says greatest common divisor of nonzero integers.

2 votes
4 answers
5k views

How to prove $5^n − 1$ is divisible by 4, for each integer n ≥ 0 by mathematical induction?

2 votes
1 answer
365 views

Find the domain and image of the relation $R=\{(a, b), (c, b), (a, b)\}$

2 votes
2 answers
237 views

Example of a relation on $X$?

2 votes
1 answer
187 views

"nonempty" in the definition of the cartesian product

2 votes
4 answers
107 views

Proving $[x \in A_i \land x \in (\forall 1\le k\le i-1: {A_k}^c)] \land [x \in A_j \land x \in (\forall 1\le k\le j-1: {A_k}^c)]$ =$\emptyset$

2 votes
2 answers
4k views

How to list elements of $\Bbb Z_j=\{x \in \Bbb Z\,|\, x-j=km \text{ for some } k \in \Bbb Z\}$ from its set builder notation?

2 votes
2 answers
485 views

How many arithematic operations(flops) are to $n×(n+1)$ matrix of system?

2 votes
1 answer
186 views

Set builder notation with $\land$?

2 votes
3 answers
146 views

Let X be the unit interval [0, 1]. Find a function $f: X \rightarrow X$ that is a symmetric relation on X.

1 vote
1 answer
163 views

Given $f: X → Y$ and $g: X → Y$ are two functions. How to prove that if $f⊆g ⇒ f=g$?

1 vote
3 answers
157 views

What's the negation of $ \ f: X\rightarrow Y\Rightarrow f(Ø)=Ø$?

1 vote
1 answer
76 views

Is proving $(f: X→ Y)\land f(\varnothing)\neq\varnothing$ is a contradiction correct in the proof of this statement?

1 vote
1 answer
257 views

Is proving "If $C⊆D⊆Y$, then $f^{-1}(C) ⊆ f^{-1}(D)$" done correctly?

1 vote
3 answers
181 views

Why "to every set and to every statement p(x), there exists {$x\in A | p(x)$}?

1 vote
1 answer
109 views

Where in the proof of this theorem shows "If (x, y)$\in f$ and (x, z) $\in f$, then y=z."?