Can we use up every whole number in the set of Natural numbers? [closed]
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In this video, Vsauce says "We've used up every single whole number, the entire infinity of them…"
Then a few seconds later he says the opposite, "You will never run out of members of either set…"
Why do these two opposite statements not contradict each other?
elementary-set-theory
asked Nov 14 at 17:27
Ivan Hieno
1339
closed as unclear what you're asking by Lord Shark the Unknown, amWhy, JMoravitz, Paul Frost, Shailesh Nov 15 at 0:04
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
-4
down vote
favorite
In this video, Vsauce says "We've used up every single whole number, the entire infinity of them…"
Then a few seconds later he says the opposite, "You will never run out of members of either set…"
Why do these two opposite statements not contradict each other?
elementary-set-theory
asked Nov 14 at 17:27
Ivan Hieno
1339
closed as unclear what you're asking by Lord Shark the Unknown, amWhy, JMoravitz, Paul Frost, Shailesh Nov 15 at 0:04
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
Doesn't sound like a contradiction to me. The contexts are different.
– saulspatz
Nov 14 at 17:29
1
I didn't watch the video, but I'm going to risk guessing that the problem lies in the definition of "using up". If by "using up" he means that every number is matched with another one, then there's no problem, such matching exists (assuming the video is correct).
– Git Gud
Nov 14 at 17:29
1
Dangerous knowledge in the information age seems to become more relevant by the day...
– Stefan Mesken
Nov 14 at 19:09
2
Find better study materials than TV.
– William Elliot
Nov 14 at 23:15
You probably won't understand this, but for the sake of completeness here's the mathematical answer. The first statement refers to the fact that there is a bijection between $mathbb Z$ and $mathbb N$, or in other words $operatorname{card}mathbb Z=operatorname{card}mathbb N$. The second refers to that $operatorname{card}mathbb Z$ is infinite (more precisely, it's $aleph_0$). These are different and noncontradictory statements.
– YiFan
Nov 15 at 4:56
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up vote
-4
down vote
favorite
up vote
-4
down vote
favorite
In this video, Vsauce says "We've used up every single whole number, the entire infinity of them…"
Then a few seconds later he says the opposite, "You will never run out of members of either set…"
Why do these two opposite statements not contradict each other?
elementary-set-theory
asked Nov 14 at 17:27
Ivan Hieno
1339
In this video, Vsauce says "We've used up every single whole number, the entire infinity of them…"
Then a few seconds later he says the opposite, "You will never run out of members of either set…"
Why do these two opposite statements not contradict each other?
elementary-set-theory
elementary-set-theory
asked Nov 14 at 17:27
Ivan Hieno
1339
asked Nov 14 at 17:27
Ivan Hieno
1339
edited Nov 15 at 3:12
asked Nov 14 at 17:27
Ivan Hieno
1339
asked Nov 14 at 17:27
Ivan Hieno
1339
asked Nov 14 at 17:27
Ivan Hieno
1339
1339
closed as unclear what you're asking by Lord Shark the Unknown, amWhy, JMoravitz, Paul Frost, Shailesh Nov 15 at 0:04
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Lord Shark the Unknown, amWhy, JMoravitz, Paul Frost, Shailesh Nov 15 at 0:04
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
Doesn't sound like a contradiction to me. The contexts are different.
– saulspatz
Nov 14 at 17:29
1
I didn't watch the video, but I'm going to risk guessing that the problem lies in the definition of "using up". If by "using up" he means that every number is matched with another one, then there's no problem, such matching exists (assuming the video is correct).
– Git Gud
Nov 14 at 17:29
1
Dangerous knowledge in the information age seems to become more relevant by the day...
– Stefan Mesken
Nov 14 at 19:09
2
Find better study materials than TV.
– William Elliot
Nov 14 at 23:15
You probably won't understand this, but for the sake of completeness here's the mathematical answer. The first statement refers to the fact that there is a bijection between $mathbb Z$ and $mathbb N$, or in other words $operatorname{card}mathbb Z=operatorname{card}mathbb N$. The second refers to that $operatorname{card}mathbb Z$ is infinite (more precisely, it's $aleph_0$). These are different and noncontradictory statements.
– YiFan
Nov 15 at 4:56
add a comment |
1
Doesn't sound like a contradiction to me. The contexts are different.
– saulspatz
Nov 14 at 17:29
1
I didn't watch the video, but I'm going to risk guessing that the problem lies in the definition of "using up". If by "using up" he means that every number is matched with another one, then there's no problem, such matching exists (assuming the video is correct).
– Git Gud
Nov 14 at 17:29
1
Dangerous knowledge in the information age seems to become more relevant by the day...
– Stefan Mesken
Nov 14 at 19:09
2
Find better study materials than TV.
– William Elliot
Nov 14 at 23:15
You probably won't understand this, but for the sake of completeness here's the mathematical answer. The first statement refers to the fact that there is a bijection between $mathbb Z$ and $mathbb N$, or in other words $operatorname{card}mathbb Z=operatorname{card}mathbb N$. The second refers to that $operatorname{card}mathbb Z$ is infinite (more precisely, it's $aleph_0$). These are different and noncontradictory statements.
– YiFan
Nov 15 at 4:56
1
1
Doesn't sound like a contradiction to me. The contexts are different.
– saulspatz
Nov 14 at 17:29
Doesn't sound like a contradiction to me. The contexts are different.
– saulspatz
Nov 14 at 17:29
1
1
I didn't watch the video, but I'm going to risk guessing that the problem lies in the definition of "using up". If by "using up" he means that every number is matched with another one, then there's no problem, such matching exists (assuming the video is correct).
– Git Gud
Nov 14 at 17:29
I didn't watch the video, but I'm going to risk guessing that the problem lies in the definition of "using up". If by "using up" he means that every number is matched with another one, then there's no problem, such matching exists (assuming the video is correct).
– Git Gud
Nov 14 at 17:29
1
1
Dangerous knowledge in the information age seems to become more relevant by the day...
– Stefan Mesken
Nov 14 at 19:09
Dangerous knowledge in the information age seems to become more relevant by the day...
– Stefan Mesken
Nov 14 at 19:09
2
2
Find better study materials than TV.
– William Elliot
Nov 14 at 23:15
Find better study materials than TV.
– William Elliot
Nov 14 at 23:15
You probably won't understand this, but for the sake of completeness here's the mathematical answer. The first statement refers to the fact that there is a bijection between $mathbb Z$ and $mathbb N$, or in other words $operatorname{card}mathbb Z=operatorname{card}mathbb N$. The second refers to that $operatorname{card}mathbb Z$ is infinite (more precisely, it's $aleph_0$). These are different and noncontradictory statements.
– YiFan
Nov 15 at 4:56
You probably won't understand this, but for the sake of completeness here's the mathematical answer. The first statement refers to the fact that there is a bijection between $mathbb Z$ and $mathbb N$, or in other words $operatorname{card}mathbb Z=operatorname{card}mathbb N$. The second refers to that $operatorname{card}mathbb Z$ is infinite (more precisely, it's $aleph_0$). These are different and noncontradictory statements.
– YiFan
Nov 15 at 4:56
add a comment |
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1
Doesn't sound like a contradiction to me. The contexts are different.
– saulspatz
Nov 14 at 17:29
1
I didn't watch the video, but I'm going to risk guessing that the problem lies in the definition of "using up". If by "using up" he means that every number is matched with another one, then there's no problem, such matching exists (assuming the video is correct).
– Git Gud
Nov 14 at 17:29
1
Dangerous knowledge in the information age seems to become more relevant by the day...
– Stefan Mesken
Nov 14 at 19:09
2
Find better study materials than TV.
– William Elliot
Nov 14 at 23:15
You probably won't understand this, but for the sake of completeness here's the mathematical answer. The first statement refers to the fact that there is a bijection between $mathbb Z$ and $mathbb N$, or in other words $operatorname{card}mathbb Z=operatorname{card}mathbb N$. The second refers to that $operatorname{card}mathbb Z$ is infinite (more precisely, it's $aleph_0$). These are different and noncontradictory statements.
– YiFan
Nov 15 at 4:56