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buzzee
  • Member for 6 years, 8 months
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16 votes
7 answers
89k views

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

0 votes
1 answer
2k views

Which is the correct notation for denoting Dom(f)? X, {$x∈X$|(x, y)$\in f$ for some y}, or {$x ∈ X$ : $∃y(y ∈Y$ ∧ (x, y) $∈ f$)}

1 vote
0 answers
79 views

How do we tell arithemetic addition or subtraction from floating point numbers?

6 votes
4 answers
17k views

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

0 votes
1 answer
135 views

Isn't x/E = y/ E ⇔ x E y deduced, not just x/E = y/ E ⇒ x E y from (a) x/ E≠ Ø, (b) x/E ∩ y/ E ≠ Ø ⇔xEy?

0 votes
5 answers
404 views

Does {$\Bbb Z_0$,$\Bbb Z_1$, $\Bbb Z_2 ,\cdots$, $\Bbb Z_{m-1}$} form a partition of $\Bbb Z$?

7 votes
1 answer
5k views

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

6 votes
2 answers
2k views

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

-1 votes
2 answers
163 views

Prove that $\{(a, a), (b, b), (c, c), (a, b), (b, a), (c, a), (a, c)\}$ is reflexive and symmetric but not transitive.

-2 votes
2 answers
131 views

Doesn't statement 'S is a set of all sets that are not elements of themselves.' hold true by reductio ad absurdum?

0 votes
3 answers
122 views

Is it okay to say 'an element of a family'?

1 vote
3 answers
159 views

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

0 votes
2 answers
77 views

Is $y \in\{f(x)\mid x \in X\} ⇔ f(x) \space ∃ x \in X$ true?

1 vote
1 answer
80 views

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

0 votes
1 answer
50 views

How does $f: X\rightarrow W$ in the Theorem 6 satisfy Def. 8(b) "If $(x, y) \in f$ and $(x, z) \in f$, then y=z"?

0 votes
1 answer
91 views

are $a$'s, $1$'s in a family $\{a, a, a\}, \{1, 2\}, \{2, 4\}$ themselves sets?

0 votes
1 answer
27 views

Can you denote a family $F: N → P(R)$ such that $F(n) = R\space, ∀n ∈ N$ in a set builder notation?

0 votes
1 answer
55 views

Can you give an example of function $F: N → P(R)$, such that $F(n) = R\space ∀n ∈ N$?

0 votes
2 answers
109 views

Which is the correct explanation? $family ⊇ set$ or $family \Leftrightarrow $a set whose elements are sets themselves

0 votes
1 answer
70 views

Can you give an example of $\bigcup\limits_{C \in \mathscr P} C=X$?

2 votes
1 answer
157 views

Set builder notation with $\land$?

1 vote
1 answer
69 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
67 views

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

2 votes
3 answers
106 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
3 answers
128 views

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

1 vote
1 answer
106 views

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

1 vote
2 answers
5k views

Why polynomial functions f(x)+g(x) = (f+g)(x)?

1 vote
1 answer
315 views

What does leading $0s$ in a number in scientific notation mean?

1 vote
1 answer
240 views

Is it correct that $n×(n+1)$ matrix takes $2n^3/3 +n^2/2-7n/6$ flops in the reduction to echelon form?

0 votes
0 answers
113 views

Why it takes at most $n$ flops to reduce a matrix a form?