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## Search found 13 matches

- Sat Sep 28, 2019 6:34 pm
- Forum: Linear Algebra
- Topic: Linear Projection
- Replies:
**2** - Views:
**729**

### Re: Linear Projection

$f=I$

- Thu Mar 30, 2017 7:53 pm
- Forum: Real Analysis
- Topic: Series and continuous functions
- Replies:
**3** - Views:
**879**

### Re: Series and continuous functions

The first function is not continuous.(no Lebesgue integrable)

The condition 2 is not true.

The sequence must be decreasing

The condition 2 is not true.

The sequence must be decreasing

- Thu Dec 15, 2016 11:21 pm
- Forum: Number theory
- Topic: Subset of natural numbers
- Replies:
**2** - Views:
**1571**

### Re: Subset of natural numbers

Why there exist $a,b\in S$ with $(a,b)=1$?

- Thu Dec 15, 2016 8:23 am
- Forum: Real Analysis
- Topic: Existence of $x$
- Replies:
**1** - Views:
**640**

### Re: Existence of $x$

What if $ \int _{A}g=0$ and $ \int _{A}fg\neq 0 $ ?

- Thu Oct 27, 2016 2:14 pm
- Forum: Real Analysis
- Topic: Bounded sequence
- Replies:
**6** - Views:
**2721**

### Re: Bounded sequence

It is not bounded near zero.

- Thu Sep 08, 2016 2:05 pm
- Forum: Algebra
- Topic: $\mathbb{R}^5$ over $\mathbb{R}$
- Replies:
**2** - Views:
**1723**

### Re: $\mathbb{R}^5$ over $\mathbb{R}$

We have

1)Every finite extension is algebraic

2)The algebraic closure of real numbers are

the complex numbers

3)Every finite extension of real numbers are

the complex numbers.

1)Every finite extension is algebraic

2)The algebraic closure of real numbers are

the complex numbers

3)Every finite extension of real numbers are

the complex numbers.

- Mon Sep 05, 2016 10:50 pm
- Forum: Algebra
- Topic: An Interesting Exercise
- Replies:
**4** - Views:
**1903**

### Re: An Interesting Exercise

1) subspace of a vector space for me( Rudin Functional Analysis and other) mean linear subspace.

2)This is a simple version of Tietze Extension Theorem.

0

2)This is a simple version of Tietze Extension Theorem.

0

- Thu Sep 01, 2016 3:05 pm
- Forum: Complex Analysis
- Topic: Non existence of complex functions
- Replies:
**3** - Views:
**1244**

### Re: Non existence of complex functions

If we restrict the function to the half-plane where ${\rm Re}(z) \geq 0$ , then $g$ is bounded which by a known fact of complex analysis means it is constant. The above is false. $g(z)=\exp(-z)$.

- Thu Sep 01, 2016 2:24 pm
- Forum: Complex Analysis
- Topic: The function $f$ is constant
- Replies:
**2** - Views:
**1188**

### Re: The function $f$ is constant

Is easy to prove:

The range of entire no constant function is dense.

The range of entire no constant function is dense.

- Tue Aug 30, 2016 3:02 pm
- Forum: Algebra
- Topic: An Interesting Exercise
- Replies:
**4** - Views:
**1903**

### Re: An Interesting Exercise

1) If X is compact then is not subspace

2)The functions in Hahn-Banach theorem are linear

2)The functions in Hahn-Banach theorem are linear