How can I prove that imaginary numbers are infinite and uncountable? [closed]

up vote
-4
down vote

favorite

Can anyone help me with this proof?

edited Dec 2 at 13:24

mrtaurho

2,7391827

asked Dec 2 at 13:20

Will_U

New contributor

closed as off-topic by GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul Dec 2 at 13:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul

If this question can be reworded to fit the rules in the help center, please edit the question.

5

Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Dec 2 at 13:20

add a comment |

up vote
-4
down vote

favorite

Can anyone help me with this proof?

edited Dec 2 at 13:24

mrtaurho

2,7391827

asked Dec 2 at 13:20

Will_U

New contributor

closed as off-topic by GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul Dec 2 at 13:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul

If this question can be reworded to fit the rules in the help center, please edit the question.

5

Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Dec 2 at 13:20

add a comment |

up vote
-4
down vote

favorite

Can anyone help me with this proof?

edited Dec 2 at 13:24

mrtaurho

2,7391827

asked Dec 2 at 13:20

Will_U

New contributor

Can anyone help me with this proof?

proof-writing cardinals

edited Dec 2 at 13:24

mrtaurho

2,7391827

asked Dec 2 at 13:20

Will_U

New contributor

edited Dec 2 at 13:24

mrtaurho

2,7391827

asked Dec 2 at 13:20

Will_U

New contributor

edited Dec 2 at 13:24

mrtaurho

2,7391827

edited Dec 2 at 13:24

mrtaurho

2,7391827

edited Dec 2 at 13:24

mrtaurho

2,7391827

asked Dec 2 at 13:20

Will_U

New contributor

asked Dec 2 at 13:20

Will_U

asked Dec 2 at 13:20

Will_U

New contributor

Will_U is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

closed as off-topic by GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul Dec 2 at 13:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul Dec 2 at 13:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, José Carlos Santos, Dietrich Burde, amWhy, Crostul

If this question can be reworded to fit the rules in the help center, please edit the question.

5

Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Dec 2 at 13:20

add a comment |

5

Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Dec 2 at 13:20

Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
– mrtaurho
Dec 2 at 13:20

add a comment |

1 Answer
1

active

oldest

votes

up vote
3
down vote

accepted

This is a bijection $f colon mathbb{R} to I$, if $I$ is the set of all imaginary numbers:
$$f(x) = xcdot i$$

If so the cardinality of $I$ is equal to the cardinality of $mathbb{R}$, and since $mathbb{R}$ is uncountably infinite so is $I$.

answered Dec 2 at 13:25

AlephZero

25816

New contributor

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

up vote
3
down vote

accepted

This is a bijection $f colon mathbb{R} to I$, if $I$ is the set of all imaginary numbers:
$$f(x) = xcdot i$$

If so the cardinality of $I$ is equal to the cardinality of $mathbb{R}$, and since $mathbb{R}$ is uncountably infinite so is $I$.

answered Dec 2 at 13:25

AlephZero

25816

New contributor

add a comment |

up vote
3
down vote

accepted

This is a bijection $f colon mathbb{R} to I$, if $I$ is the set of all imaginary numbers:
$$f(x) = xcdot i$$

If so the cardinality of $I$ is equal to the cardinality of $mathbb{R}$, and since $mathbb{R}$ is uncountably infinite so is $I$.

answered Dec 2 at 13:25

AlephZero

25816

New contributor

add a comment |

up vote
3
down vote

accepted

This is a bijection $f colon mathbb{R} to I$, if $I$ is the set of all imaginary numbers:
$$f(x) = xcdot i$$

If so the cardinality of $I$ is equal to the cardinality of $mathbb{R}$, and since $mathbb{R}$ is uncountably infinite so is $I$.

answered Dec 2 at 13:25

AlephZero

25816

New contributor

This is a bijection $f colon mathbb{R} to I$, if $I$ is the set of all imaginary numbers:
$$f(x) = xcdot i$$

If so the cardinality of $I$ is equal to the cardinality of $mathbb{R}$, and since $mathbb{R}$ is uncountably infinite so is $I$.

answered Dec 2 at 13:25

AlephZero

25816

New contributor

answered Dec 2 at 13:25

AlephZero

25816

New contributor

answered Dec 2 at 13:25

AlephZero

25816

answered Dec 2 at 13:25

AlephZero

25816

New contributor

AlephZero is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

add a comment |

This page is only for reference, If you need detailed information, please check here

搜尋此網誌

Xrfgtjtk