Lining up. Can you draw a line segment that has more points than the line segment L? L_________

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Answer 1

Textbook Question

Chapter 3.5, Problem 1MS

Lining up. Can you draw a line segment that has more points than the line segment L?

L_________

Expert Solution & Answer

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer to Problem 1MS

No, it is not possible to draw such line.

Explanation of Solution

Given information:

A line segment L is given by

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 1

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 2

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.

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Answer 2

Textbook Question

Chapter 3.5, Problem 1MS

Lining up. Can you draw a line segment that has more points than the line segment L?

L_________

Expert Solution & Answer

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer to Problem 1MS

No, it is not possible to draw such line.

Explanation of Solution

Given information:

A line segment L is given by

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 1

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 2

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 3.5, Problem 1MS

Lining up. Can you draw a line segment that has more points than the line segment L?

L_________

Expert Solution & Answer

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer to Problem 1MS

No, it is not possible to draw such line.

Explanation of Solution

Given information:

A line segment L is given by

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 1

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 2

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 3.5, Problem 1MS

Lining up. Can you draw a line segment that has more points than the line segment L?

L_________

Expert Solution & Answer

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer to Problem 1MS

No, it is not possible to draw such line.

Explanation of Solution

Given information:

A line segment L is given by

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 1

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 2

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer to Problem 1MS

No, it is not possible to draw such line.

Explanation of Solution

Given information:

A line segment L is given by

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 1

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 2

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.

Answer 8

Expert Solution & Answer

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer to Problem 1MS

No, it is not possible to draw such line.

Explanation of Solution

Given information:

A line segment L is given by

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 1

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 2

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer 12

Answer to Problem 1MS

No, it is not possible to draw such line.

Answer 13

Explanation of Solution

Given information:

A line segment L is given by

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 1

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

The Heart of Mathematics: An Invitation to Effective Thinking, Chapter 3.5, Problem 1MS , additional homework tip 2

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.