bradley_spring22: formula evidence

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181 rows

Inline formulas (first occurrence) (181)

The page, the confidence and the picture of an inline formula are its HOST LINE's --- a formula has none of its own. A line's confidence is not a formula's.

Identifier	Page	Conf.	LaTeX source
bradley_spring22_FO0001	3	1.000	p
bradley_spring22_FO0002	3	1.000	1 / p
bradley_spring22_FO0003	3	1.000	p=1
bradley_spring22_FO0004	3	1.000	1 / p=1 / 1=1
bradley_spring22_FO0005	3	1.000	\log (1 / p)=\log (1)=0
bradley_spring22_FO0006	3	1.000	\log (1 / p)
bradley_spring22_FO0007	3	1.000	x
bradley_spring22_FO0008	3	1.000	\log (x)
bradley_spring22_FO0009	3	1.000	\log (1)=0
bradley_spring22_FO0010	6	1.000	2 \times 3=6
bradley_spring22_FO0011	6	1.000	y
bradley_spring22_FO0012	6	1.000	x \times y
bradley_spring22_FO0013	7	1.000	x y
bradley_spring22_FO0014	7	1.000	\left(x^{3}\right)^{2} y^{4} x^{-1}
bradley_spring22_FO0015	7	1.000	x^{2}+7 x+12^{\prime \prime}
bradley_spring22_FO0016	7	1.000	(2 \times 3) \times 5
bradley_spring22_FO0017	7	1.000	2 \times(3 \times 5)
bradley_spring22_FO0018	7	0.985	A_{\infty}
bradley_spring22_FO0019	8	1.000	20=19.999 \ldots
bradley_spring22_FO0020	9	0.982	X^{\prime \prime}
bradley_spring22_FO0021	9	0.983	X
bradley_spring22_FO0022	10	0.803	\left(\frac{1}{2}, \frac{1}{2}\right)
bradley_spring22_FO0023	10	0.803	\left(\frac{2}{5}, \frac{1}{2}, \frac{1}{10}\right)
bradley_spring22_FO0024	10	1.000	(7,3)
bradley_spring22_FO0025	10	1.000	\left(-\frac{2}{5},-\frac{1}{2},-\frac{1}{10}\right)
bradley_spring22_FO0026	10	1.000	\frac{1}{2}
bradley_spring22_FO0027	10	1.000	\frac{2}{5}, \frac{1}{2}
bradley_spring22_FO0028	10	1.000	\frac{1}{10}
bradley_spring22_FO0029	10	0.960	n
bradley_spring22_FO0030	10	0.997	\{1,2, \ldots, n\}
bradley_spring22_FO0031	10	0.997	p=\left(p_{1}, p_{2}, \ldots, p_{n}\right)
bradley_spring22_FO0032	11	1.000	p_{1}+p_{2}+\cdots+p_{n}=1
bradley_spring22_FO0033	11	0.917	\left(p_{1}, p_{2}, \ldots, p_{n}\right)
bradley_spring22_FO0034	11	1.000	n=2
bradley_spring22_FO0035	11	1.000	\{1,2\}
bradley_spring22_FO0036	11	1.000	p_{1}=\frac{1}{2}
bradley_spring22_FO0037	11	1.000	p_{2}=\frac{1}{2}
bradley_spring22_FO0038	11	1.000	p=\left(p_{1}, p_{2}\right)
bradley_spring22_FO0039	11	1.000	p=\left(\frac{1}{2}, \frac{1}{2}\right)
bradley_spring22_FO0040	11	1.000	H(p)
bradley_spring22_FO0041	12	0.966	\log (1)-\log (p)
bradley_spring22_FO0042	12	0.966	-\log (p)
bradley_spring22_FO0043	12	1.000	-\log \left(p_{1}\right)
bradley_spring22_FO0044	12	1.000	-\log \left(p_{2}\right)
bradley_spring22_FO0045	12	0.983	\operatorname{logarithm} \log (p)
bradley_spring22_FO0046	12	1.000	p=(1,0)
bradley_spring22_FO0047	12	1.000	\frac{1}{n}
bradley_spring22_FO0048	12	1.000	\left(\frac{1}{n}, \frac{1}{n}, \ldots, \frac{1}{n}\right)
bradley_spring22_FO0049	12	1.000	\log (n)
bradley_spring22_FO0050	12	1.000	0 \leq H(p) \leq \log (n)
bradley_spring22_FO0051	13	1.000	H
bradley_spring22_FO0052	13	1.000	\Delta_{n}
bradley_spring22_FO0053	13	1.000	\Delta^{n-1}
bradley_spring22_FO0054	13	1.000	\mathbb{R}
bradley_spring22_FO0055	13	1.000	H: \Delta_{n} \rightarrow \mathbb{R}
bradley_spring22_FO0056	13	1.000	f: X \rightarrow Y
bradley_spring22_FO0057	13	1.000	f
bradley_spring22_FO0058	13	1.000	Y
bradley_spring22_FO0059	13	1.000	f(x)
bradley_spring22_FO0060	14	0.979	n=1,2,3, \ldots
bradley_spring22_FO0061	14	1.000	H_{n}
bradley_spring22_FO0062	14	1.000	H: \Delta_{1} \rightarrow \mathbb{R}
bradley_spring22_FO0063	14	1.000	H: \Delta_{2} \rightarrow \mathbb{R}
bradley_spring22_FO0064	14	1.000	H: \Delta_{3} \rightarrow \mathbb{R}
bradley_spring22_FO0065	14	1.000	\Delta_{1}, \Delta_{2}, \Delta_{3}, \ldots
bradley_spring22_FO0066	14	1.000	\Delta_{1}
bradley_spring22_FO0067	14	1.000	\Delta_{2}
bradley_spring22_FO0068	14	1.000	\Delta_{3}
bradley_spring22_FO0069	14	1.000	\Delta_{4}
bradley_spring22_FO0070	14	1.000	n=1
bradley_spring22_FO0071	15	0.985	x, y
bradley_spring22_FO0072	15	0.985	x+y=1
bradley_spring22_FO0073	15	1.000	y=1-x
bradley_spring22_FO0074	15	1.000	n=3
bradley_spring22_FO0075	15	0.999	x, y, z
bradley_spring22_FO0076	15	0.922	x+y+z=1
bradley_spring22_FO0077	15	0.922	z=1-x-y
bradley_spring22_FO0078	15	1.000	n=4
bradley_spring22_FO0079	15	1.000	n-1
bradley_spring22_FO0080	17	0.516	10 \%
bradley_spring22_FO0081	17	1.000	q=\left(\frac{2}{5}, \frac{1}{2}, \frac{1}{10}\right)
bradley_spring22_FO0082	17	1.000	r=\left(\frac{3}{10}, \frac{7}{10}\right)
bradley_spring22_FO0083	17	1.000	q
bradley_spring22_FO0084	17	1.000	r
bradley_spring22_FO0085	17	0.977	\frac{1}{2} \times \frac{2}{5}=\frac{1}{5}
bradley_spring22_FO0086	17	1.000	\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}
bradley_spring22_FO0087	17	0.988	\frac{1}{2} \times \frac{1}{10}=\frac{1}{20}
bradley_spring22_FO0088	17	1.000	\frac{3}{20}
bradley_spring22_FO0089	17	1.000	\frac{7}{20}
bradley_spring22_FO0090	17	1.000	\left(\frac{1}{5}, \frac{1}{4}, \frac{1}{20}, \frac{3}{20}, \frac{7}{20}\right)
bradley_spring22_FO0091	17	1.000	\Delta_{5}
bradley_spring22_FO0092	18	0.999	p \times(q, r)
bradley_spring22_FO0093	20	1.000	f: \mathbb{R}^{2} \rightarrow \mathbb{R}
bradley_spring22_FO0094	20	0.856	(x, y)
bradley_spring22_FO0095	20	0.856	f(x, y)=x y
bradley_spring22_FO0096	20	1.000	p=
bradley_spring22_FO0097	20	0.999	f: \mathbb{R}^{n} \rightarrow \mathbb{R}
bradley_spring22_FO0098	20	1.000	x=\left(x_{1}, x_{2}, \ldots, x_{n}\right)
bradley_spring22_FO0099	20	1.000	p_{1}, p_{2}, \ldots, p_{n}
bradley_spring22_FO0100	20	1.000	x=
bradley_spring22_FO0101	20	0.995	\left(x_{1}, x_{2}, \ldots, x_{n}\right)
bradley_spring22_FO0102	20	0.995	p_{1} x_{1}+p_{2} x_{2}+\cdots+p_{n} x_{n}
bradley_spring22_FO0103	21	1.000	p, q
bradley_spring22_FO0104	21	1.000	p \circ(q, r)
bradley_spring22_FO0105	21	1.000	H(p \circ(q, r))
bradley_spring22_FO0106	21	1.000	H(q)
bradley_spring22_FO0107	21	1.000	H(r)
bradley_spring22_FO0108	21	1.000	H(p \circ(q, r)) \stackrel{?}{=} H(p)+H(q)+H(r)
bradley_spring22_FO0109	22	1.000	q^{1}, q^{2}, \ldots, q^{n}
bradley_spring22_FO0110	22	1.000	p_{1}
bradley_spring22_FO0111	22	1.000	q^{1}
bradley_spring22_FO0112	22	1.000	q^{2}
bradley_spring22_FO0113	22	1.000	\Delta_{17}
bradley_spring22_FO0114	22	1.000	q^{3}
bradley_spring22_FO0115	22	1.000	p \circ\left(q^{1}, q^{2}, \ldots, q^{n}\right)
bradley_spring22_FO0116	22	1.000	\left\{F: \Delta_{n} \rightarrow\right.
bradley_spring22_FO0117	22	1.000	\mathbb{R}\}
bradley_spring22_FO0118	22	1.000	F
bradley_spring22_FO0119	22	1.000	F=c H
bradley_spring22_FO0120	22	1.000	c
bradley_spring22_FO0121	23	1.000	\left\{F: \Delta_{n} \rightarrow \mathbb{R}\right\}_{n \geq 1}
bradley_spring22_FO0122	23	1.000	H(p \circ q)=H(p)+H(q)
bradley_spring22_FO0123	23	0.998	\circ
bradley_spring22_FO0124	23	0.641	f(\bullet \bullet)=f(\bullet) f(\bullet)
bradley_spring22_FO0125	23	0.641	\bullet
bradley_spring22_FO0126	23	1.000	p \circ q=q
bradley_spring22_FO0127	23	1.000	H(p)=0
bradley_spring22_FO0128	23	1.000	H(q)=H(q)
bradley_spring22_FO0129	24	1.000	q^{1}=q
bradley_spring22_FO0130	24	1.000	q^{2}=r
bradley_spring22_FO0131	25	1.000	f: \mathbb{R} \rightarrow \mathbb{R}
bradley_spring22_FO0132	25	1.000	f^{\prime}
bradley_spring22_FO0133	25	1.000	\frac{d f}{d x}
bradley_spring22_FO0134	25	1.000	d(f)
bradley_spring22_FO0135	25	1.000	g
bradley_spring22_FO0136	25	1.000	(f g)^{\prime}
bradley_spring22_FO0137	25	1.000	g^{\prime}
bradley_spring22_FO0138	25	0.999	(f g)^{\prime}(x)=f^{\prime}(x) g(x)+f(x) g^{\prime}(x)
bradley_spring22_FO0139	25	0.978	f g
bradley_spring22_FO0140	25	1.000	d(f g)=d(f) g+f d(g)
bradley_spring22_FO0141	25	1.000	d
bradley_spring22_FO0142	25	0.322	d(\bullet \bullet)=d(\bullet) \bullet+\bullet d(\bullet)
bradley_spring22_FO0143	25	1.000	A
bradley_spring22_FO0144	25	0.737	[0,1]
bradley_spring22_FO0145	25	1.000	d:[0,1] \rightarrow \mathbb{R}
bradley_spring22_FO0146	25	1.000	d(x)=-x \log (x)
bradley_spring22_FO0147	25	1.000	x>0
bradley_spring22_FO0148	25	1.000	d(x)=0
bradley_spring22_FO0149	25	1.000	x=0
bradley_spring22_FO0150	25	0.958	d(x y)=d(x) y+x d(y)
bradley_spring22_FO0151	26	1.000	d: A \rightarrow A
bradley_spring22_FO0152	26	1.000	d(a b)=d(a) b+a d(b)
bradley_spring22_FO0153	26	1.000	a
bradley_spring22_FO0154	26	1.000	b
bradley_spring22_FO0155	26	0.996	M
bradley_spring22_FO0156	26	0.996	A^{\prime \prime}
bradley_spring22_FO0157	26	0.996	d: A \rightarrow M
bradley_spring22_FO0158	26	1.000	d(a)
bradley_spring22_FO0159	26	1.000	d(a) b
bradley_spring22_FO0160	26	1.000	a d(b)
bradley_spring22_FO0161	26	1.000	0.5 \times 8=4
bradley_spring22_FO0162	26	0.960	0.5 \times
bradley_spring22_FO0163	26	1.000	d(b)
bradley_spring22_FO0164	26	0.848	\mathbf{v}
bradley_spring22_FO0165	26	0.848	k
bradley_spring22_FO0166	27	1.000	\left\{H: \Delta_{n} \rightarrow \mathbb{R}\right\}
bradley_spring22_FO0167	27	0.947	\left\{d: \Delta_{n} \rightarrow \boldsymbol{-}\right\}
bradley_spring22_FO0168	27	1.000	d(p): \mathbb{R}^{n} \rightarrow \mathbb{R}
bradley_spring22_FO0169	27	1.000	\mathbb{R}^{n}
bradley_spring22_FO0170	27	0.921	\operatorname{hom}\left(\mathbb{R}^{n}, \mathbb{R}\right)
bradley_spring22_FO0171	27	1.000	\left\{d: \Delta_{n} \rightarrow \operatorname{hom}\left(\mathbb{R}^{n}, \mathbb{R}\right)\right\}
bradley_spring22_FO0172	27	1.000	d(p \circ q)=d(p) \circ q+q \circ d(q)
bradley_spring22_FO0173	27	1.000	p \circ q
bradley_spring22_FO0174	27	1.000	d(p) \circ q
bradley_spring22_FO0175	27	1.000	q \circ d(q)
bradley_spring22_FO0176	27	1.000	d(q)
bradley_spring22_FO0177	27	1.000	\mathbb{R}^{n} \rightarrow \mathbb{R}
bradley_spring22_FO0178	28	1.000	d\left(p \circ\left(q^{1}, q^{2}, \ldots, q^{n}\right)\right)
bradley_spring22_FO0179	29	1.000	d(p)(x)=H(p)
bradley_spring22_FO0180	29	1.000	d(p)(x)=c H(p)
bradley_spring22_FO0181	29	1.000	d(p)(0)=c H(p)

Identifier

Page

Conf.

LaTeX source

Rendered

Image

bradley_spring22_FO0001

1.000

bradley_spring22_FO0002

1.000

1 / p

bradley_spring22_FO0003

1.000

p=1

bradley_spring22_FO0004

1.000

1 / p=1 / 1=1

bradley_spring22_FO0005

1.000

\log (1 / p)=\log (1)=0

bradley_spring22_FO0006

1.000

\log (1 / p)

bradley_spring22_FO0007

1.000

bradley_spring22_FO0008

1.000

\log (x)

bradley_spring22_FO0009

1.000

\log (1)=0

bradley_spring22_FO0010

1.000

2 \times 3=6

bradley_spring22_FO0011

1.000

bradley_spring22_FO0012

1.000

x \times y

bradley_spring22_FO0013

1.000

x y

bradley_spring22_FO0014

1.000

\left(x^{3}\right)^{2} y^{4} x^{-1}

bradley_spring22_FO0015

1.000

x^{2}+7 x+12^{\prime \prime}

bradley_spring22_FO0016

1.000

(2 \times 3) \times 5

bradley_spring22_FO0017

1.000

2 \times(3 \times 5)

bradley_spring22_FO0018

0.985

A_{\infty}

bradley_spring22_FO0019

1.000

20=19.999 \ldots

bradley_spring22_FO0020

0.982

X^{\prime \prime}

bradley_spring22_FO0021

0.983

bradley_spring22_FO0022

0.803

\left(\frac{1}{2}, \frac{1}{2}\right)

bradley_spring22_FO0023

0.803

\left(\frac{2}{5}, \frac{1}{2}, \frac{1}{10}\right)

bradley_spring22_FO0024

1.000

(7,3)

bradley_spring22_FO0025

1.000

\left(-\frac{2}{5},-\frac{1}{2},-\frac{1}{10}\right)

bradley_spring22_FO0026

1.000

\frac{1}{2}

bradley_spring22_FO0027

1.000

\frac{2}{5}, \frac{1}{2}

bradley_spring22_FO0028

1.000

\frac{1}{10}

bradley_spring22_FO0029

0.960

bradley_spring22_FO0030

0.997

\{1,2, \ldots, n\}

bradley_spring22_FO0031

0.997

p=\left(p_{1}, p_{2}, \ldots, p_{n}\right)

bradley_spring22_FO0032

1.000

p_{1}+p_{2}+\cdots+p_{n}=1

bradley_spring22_FO0033

0.917

\left(p_{1}, p_{2}, \ldots, p_{n}\right)

bradley_spring22_FO0034

1.000

n=2

bradley_spring22_FO0035

1.000

\{1,2\}

bradley_spring22_FO0036

1.000

p_{1}=\frac{1}{2}

bradley_spring22_FO0037

1.000

p_{2}=\frac{1}{2}

bradley_spring22_FO0038

1.000

p=\left(p_{1}, p_{2}\right)

bradley_spring22_FO0039

1.000

p=\left(\frac{1}{2}, \frac{1}{2}\right)

bradley_spring22_FO0040

1.000

H(p)

bradley_spring22_FO0041

0.966

\log (1)-\log (p)

bradley_spring22_FO0042

0.966

-\log (p)

bradley_spring22_FO0043

1.000

-\log \left(p_{1}\right)

bradley_spring22_FO0044

1.000

-\log \left(p_{2}\right)

bradley_spring22_FO0045

0.983

\operatorname{logarithm} \log (p)

bradley_spring22_FO0046

1.000

p=(1,0)

bradley_spring22_FO0047

1.000

\frac{1}{n}

bradley_spring22_FO0048

1.000

\left(\frac{1}{n}, \frac{1}{n}, \ldots, \frac{1}{n}\right)

bradley_spring22_FO0049

1.000

\log (n)

bradley_spring22_FO0050

1.000

0 \leq H(p) \leq \log (n)

bradley_spring22_FO0051

1.000

bradley_spring22_FO0052

1.000

\Delta_{n}

bradley_spring22_FO0053

1.000

\Delta^{n-1}

bradley_spring22_FO0054

1.000

\mathbb{R}

bradley_spring22_FO0055

1.000

H: \Delta_{n} \rightarrow \mathbb{R}

bradley_spring22_FO0056

1.000

f: X \rightarrow Y

bradley_spring22_FO0057

1.000

bradley_spring22_FO0058

1.000

bradley_spring22_FO0059

1.000

f(x)

bradley_spring22_FO0060

0.979

n=1,2,3, \ldots

bradley_spring22_FO0061

1.000

H_{n}

bradley_spring22_FO0062

1.000

H: \Delta_{1} \rightarrow \mathbb{R}

bradley_spring22_FO0063

1.000

H: \Delta_{2} \rightarrow \mathbb{R}

bradley_spring22_FO0064

1.000

H: \Delta_{3} \rightarrow \mathbb{R}

bradley_spring22_FO0065

1.000

\Delta_{1}, \Delta_{2}, \Delta_{3}, \ldots

bradley_spring22_FO0066

1.000

\Delta_{1}

bradley_spring22_FO0067

1.000

\Delta_{2}

bradley_spring22_FO0068

1.000

\Delta_{3}

bradley_spring22_FO0069

1.000

\Delta_{4}

bradley_spring22_FO0070

1.000

n=1

bradley_spring22_FO0071

0.985

x, y

bradley_spring22_FO0072

0.985

x+y=1

bradley_spring22_FO0073

1.000

y=1-x

bradley_spring22_FO0074

1.000

n=3

bradley_spring22_FO0075

0.999

x, y, z

bradley_spring22_FO0076

0.922

x+y+z=1

bradley_spring22_FO0077

0.922

z=1-x-y

bradley_spring22_FO0078

1.000

n=4

bradley_spring22_FO0079

1.000

n-1

bradley_spring22_FO0080

0.516

10 \%

bradley_spring22_FO0081

1.000

q=\left(\frac{2}{5}, \frac{1}{2}, \frac{1}{10}\right)

bradley_spring22_FO0082

1.000

r=\left(\frac{3}{10}, \frac{7}{10}\right)

bradley_spring22_FO0083

1.000

bradley_spring22_FO0084

1.000

bradley_spring22_FO0085

0.977

\frac{1}{2} \times \frac{2}{5}=\frac{1}{5}

bradley_spring22_FO0086

1.000

\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}

bradley_spring22_FO0087

0.988

\frac{1}{2} \times \frac{1}{10}=\frac{1}{20}

bradley_spring22_FO0088

1.000

\frac{3}{20}

bradley_spring22_FO0089

1.000

\frac{7}{20}

bradley_spring22_FO0090

1.000

\left(\frac{1}{5}, \frac{1}{4}, \frac{1}{20}, \frac{3}{20}, \frac{7}{20}\right)

bradley_spring22_FO0091

1.000

\Delta_{5}

bradley_spring22_FO0092

0.999

p \times(q, r)

bradley_spring22_FO0093

1.000

f: \mathbb{R}^{2} \rightarrow \mathbb{R}

bradley_spring22_FO0094

0.856

(x, y)

bradley_spring22_FO0095

0.856

f(x, y)=x y

bradley_spring22_FO0096

1.000

bradley_spring22_FO0097

0.999

f: \mathbb{R}^{n} \rightarrow \mathbb{R}

bradley_spring22_FO0098

1.000

x=\left(x_{1}, x_{2}, \ldots, x_{n}\right)

bradley_spring22_FO0099

1.000

p_{1}, p_{2}, \ldots, p_{n}

bradley_spring22_FO0100

1.000

bradley_spring22_FO0101

0.995

\left(x_{1}, x_{2}, \ldots, x_{n}\right)

bradley_spring22_FO0102

0.995

p_{1} x_{1}+p_{2} x_{2}+\cdots+p_{n} x_{n}

bradley_spring22_FO0103

1.000

p, q

bradley_spring22_FO0104

1.000

p \circ(q, r)

bradley_spring22_FO0105

1.000

H(p \circ(q, r))

bradley_spring22_FO0106

1.000

H(q)

bradley_spring22_FO0107

1.000

H(r)

bradley_spring22_FO0108

1.000

H(p \circ(q, r)) \stackrel{?}{=} H(p)+H(q)+H(r)

bradley_spring22_FO0109

1.000

q^{1}, q^{2}, \ldots, q^{n}

bradley_spring22_FO0110

1.000

p_{1}

bradley_spring22_FO0111

1.000

q^{1}

bradley_spring22_FO0112

1.000

q^{2}

bradley_spring22_FO0113

1.000

\Delta_{17}

bradley_spring22_FO0114

1.000

q^{3}

bradley_spring22_FO0115

1.000

p \circ\left(q^{1}, q^{2}, \ldots, q^{n}\right)

bradley_spring22_FO0116

1.000

\left\{F: \Delta_{n} \rightarrow\right.

bradley_spring22_FO0117

1.000

\mathbb{R}\}

bradley_spring22_FO0118

1.000

bradley_spring22_FO0119

1.000

F=c H

bradley_spring22_FO0120

1.000

bradley_spring22_FO0121

1.000

\left\{F: \Delta_{n} \rightarrow \mathbb{R}\right\}_{n \geq 1}

bradley_spring22_FO0122

1.000

H(p \circ q)=H(p)+H(q)

bradley_spring22_FO0123

0.998

\circ

bradley_spring22_FO0124

0.641

f(\bullet \bullet)=f(\bullet) f(\bullet)

bradley_spring22_FO0125

0.641

\bullet

bradley_spring22_FO0126

1.000

p \circ q=q

bradley_spring22_FO0127

1.000

H(p)=0

bradley_spring22_FO0128

1.000

H(q)=H(q)

bradley_spring22_FO0129

1.000

q^{1}=q

bradley_spring22_FO0130

1.000

q^{2}=r

bradley_spring22_FO0131

1.000

f: \mathbb{R} \rightarrow \mathbb{R}

bradley_spring22_FO0132

1.000

f^{\prime}

bradley_spring22_FO0133

1.000

\frac{d f}{d x}

bradley_spring22_FO0134

1.000

d(f)

bradley_spring22_FO0135

1.000

bradley_spring22_FO0136

1.000

(f g)^{\prime}

bradley_spring22_FO0137

1.000

g^{\prime}

bradley_spring22_FO0138

0.999

(f g)^{\prime}(x)=f^{\prime}(x) g(x)+f(x) g^{\prime}(x)

bradley_spring22_FO0139

0.978

f g

bradley_spring22_FO0140

1.000

d(f g)=d(f) g+f d(g)

bradley_spring22_FO0141

1.000

bradley_spring22_FO0142

0.322

d(\bullet \bullet)=d(\bullet) \bullet+\bullet d(\bullet)

bradley_spring22_FO0143

1.000

bradley_spring22_FO0144

0.737

[0,1]

bradley_spring22_FO0145

1.000

d:[0,1] \rightarrow \mathbb{R}

bradley_spring22_FO0146

1.000

d(x)=-x \log (x)

bradley_spring22_FO0147

1.000

x>0

bradley_spring22_FO0148

1.000

d(x)=0

bradley_spring22_FO0149

1.000

x=0

bradley_spring22_FO0150

0.958

d(x y)=d(x) y+x d(y)

bradley_spring22_FO0151

1.000

d: A \rightarrow A

bradley_spring22_FO0152

1.000

d(a b)=d(a) b+a d(b)

bradley_spring22_FO0153

1.000

bradley_spring22_FO0154

1.000

bradley_spring22_FO0155

0.996

bradley_spring22_FO0156

0.996

A^{\prime \prime}

bradley_spring22_FO0157

0.996

d: A \rightarrow M

bradley_spring22_FO0158

1.000

d(a)

bradley_spring22_FO0159

1.000

d(a) b

bradley_spring22_FO0160

1.000

a d(b)

bradley_spring22_FO0161

1.000

0.5 \times 8=4

bradley_spring22_FO0162

0.960

0.5 \times

bradley_spring22_FO0163

1.000

d(b)

bradley_spring22_FO0164

0.848

\mathbf{v}

bradley_spring22_FO0165

0.848

bradley_spring22_FO0166

1.000

\left\{H: \Delta_{n} \rightarrow \mathbb{R}\right\}

bradley_spring22_FO0167

0.947

\left\{d: \Delta_{n} \rightarrow \boldsymbol{-}\right\}

bradley_spring22_FO0168

1.000

d(p): \mathbb{R}^{n} \rightarrow \mathbb{R}

bradley_spring22_FO0169

1.000

\mathbb{R}^{n}

bradley_spring22_FO0170

0.921

\operatorname{hom}\left(\mathbb{R}^{n}, \mathbb{R}\right)

bradley_spring22_FO0171

1.000

\left\{d: \Delta_{n} \rightarrow \operatorname{hom}\left(\mathbb{R}^{n}, \mathbb{R}\right)\right\}

bradley_spring22_FO0172

1.000

d(p \circ q)=d(p) \circ q+q \circ d(q)

bradley_spring22_FO0173

1.000

p \circ q

bradley_spring22_FO0174

1.000

d(p) \circ q

bradley_spring22_FO0175

1.000

q \circ d(q)

bradley_spring22_FO0176

1.000

d(q)

bradley_spring22_FO0177

1.000

\mathbb{R}^{n} \rightarrow \mathbb{R}

bradley_spring22_FO0178

1.000

d\left(p \circ\left(q^{1}, q^{2}, \ldots, q^{n}\right)\right)

bradley_spring22_FO0179

1.000

d(p)(x)=H(p)

bradley_spring22_FO0180

1.000

d(p)(x)=c H(p)

bradley_spring22_FO0181

1.000

d(p)(0)=c H(p)