Fdtxjr

If the only attacker is removed from combat, is a creature still counted as having attacked this turn?

Telemetry for feature health

Overlapping circles covering polygon

What happens if I try to grapple mirror image?

Proving an identity involving cross products and coplanar vectors

Review your own paper in Mathematics

Why does the Persian emissary display a string of crowned skulls?

How many people need to be born every 8 years to sustain population?

Origin of pigs as a species

Mimic lecturing on blackboard, facing audience

Difference between shutdown options

SOQL query causes internal Salesforce error

Can I say "fingers" when referring to toes?

What does "tick" mean in this sentence?

How to get directions in deep space?

Identifying "long and narrow" polygons in with PostGIS

What is this high flying aircraft over Pennsylvania?

How do I tell my boss that I'm quitting in 15 days (a colleague left this week)

Is there a RAID 0 Equivalent for RAM?

Language involving irrational number is not a CFL

Unable to disable Microsoft Store in domain environment

Should I warn a new PhD Student?

What should be the ideal length of sentences in a blog post for ease of reading?

Is there a distance limit for minecart tracks?

$e^x neq 0$ Proof Correctness

Correctness of proof of division in ceiling functionCorrectness of Proof by RefutationProve that $ 2^n not equiv 1 pmodn $ for any $n > 1$.Proof of Correctness of Recursive AlgorithmProof about the convergence of a sequenceTowers of Hanoi - Proof of CorrectnessIs this proof for $e^ipi=-1$ correct?Proof in constructive mathematics using decidability.Is this proof of irrationality?A Proof for Generalized Rolle's Theorem

0

$begingroup$

note: I’m not looking for another proof for this, I am just asking if this proof is correct.

This is my proof.

Assume $f(x)=e^x=0$

Then $e^fracx2e^fracx2=0$

More generally, $(e^fracxn)^n=0$

$lim_n to inftyf(x)=lim_n to infty1^n=1$

That means $1=0$ hence the contradiction.

limits proof-verification exponential-function

share|cite|improve this question

edited Mar 14 at 7:11

José Carlos Santos

169k23132237

asked Mar 14 at 5:58

Simplex1Simplex1

404

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't follow the proof since the first limit, should it be $lim_n to infty f(x/n)$ perhaps? And why does that come out to $1^n$?
  $endgroup$
  – Joppy
  Mar 14 at 6:02
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Joppy It comes out to $1^n$ because I took the limit of $e^fracxn$ first which equals 1.
  $endgroup$
  – Simplex1
  Mar 14 at 6:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is quite clear from the expansion of $e^x$ that $e^x > 0$ for $x>0$ Now observe that $e^xcdot e^-x = 1.$ So $e^-x neq 0.$
  $endgroup$
  – Dbchatto67
  Mar 14 at 6:04
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can't evaluate limits like $(e^fracxn)^n$ "one at a time"
  $endgroup$
  – Joppy
  Mar 14 at 6:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why cant you do that?
  $endgroup$
  – Simplex1
  Mar 14 at 6:08
  

  
  
  
  

 | 
show 1 more comment

0

$begingroup$

note: I’m not looking for another proof for this, I am just asking if this proof is correct.

This is my proof.

Assume $f(x)=e^x=0$

Then $e^fracx2e^fracx2=0$

More generally, $(e^fracxn)^n=0$

$lim_n to inftyf(x)=lim_n to infty1^n=1$

That means $1=0$ hence the contradiction.

limits proof-verification exponential-function

share|cite|improve this question

edited Mar 14 at 7:11

José Carlos Santos

169k23132237

asked Mar 14 at 5:58

Simplex1Simplex1

404

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't follow the proof since the first limit, should it be $lim_n to infty f(x/n)$ perhaps? And why does that come out to $1^n$?
  $endgroup$
  – Joppy
  Mar 14 at 6:02
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Joppy It comes out to $1^n$ because I took the limit of $e^fracxn$ first which equals 1.
  $endgroup$
  – Simplex1
  Mar 14 at 6:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is quite clear from the expansion of $e^x$ that $e^x > 0$ for $x>0$ Now observe that $e^xcdot e^-x = 1.$ So $e^-x neq 0.$
  $endgroup$
  – Dbchatto67
  Mar 14 at 6:04
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can't evaluate limits like $(e^fracxn)^n$ "one at a time"
  $endgroup$
  – Joppy
  Mar 14 at 6:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why cant you do that?
  $endgroup$
  – Simplex1
  Mar 14 at 6:08
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

note: I’m not looking for another proof for this, I am just asking if this proof is correct.

This is my proof.

Assume $f(x)=e^x=0$

Then $e^fracx2e^fracx2=0$

More generally, $(e^fracxn)^n=0$

$lim_n to inftyf(x)=lim_n to infty1^n=1$

That means $1=0$ hence the contradiction.

limits proof-verification exponential-function

share|cite|improve this question

edited Mar 14 at 7:11

José Carlos Santos

169k23132237

asked Mar 14 at 5:58

Simplex1Simplex1

404

$endgroup$

share|cite|improve this question

edited Mar 14 at 7:11

José Carlos Santos

169k23132237

asked Mar 14 at 5:58

Simplex1Simplex1

404

share|cite|improve this question

edited Mar 14 at 7:11

José Carlos Santos

169k23132237

asked Mar 14 at 5:58

Simplex1Simplex1

404

edited Mar 14 at 7:11

José Carlos Santos

169k23132237

edited Mar 14 at 7:11

José Carlos Santos

169k23132237

asked Mar 14 at 5:58

Simplex1Simplex1

404

asked Mar 14 at 5:58

Simplex1Simplex1

404

1 Answer
1

active

oldest

votes

7

$begingroup$

The proof is not correct because it assumes implicitely that if a sequence $(a_n)_ninmathbb N$ converges to $1$, then $lim_ntoinftya_n^n=1$. This is not true. For instance,$$lim_ntoinfty left (1 + frac1n right )=1text and lim_ntoinftyleft(1 + frac1nright)^n=eneq1.$$

share|cite|improve this answer

edited Mar 14 at 6:22

Dbchatto67

1,995319

answered Mar 14 at 6:16

José Carlos SantosJosé Carlos Santos

169k23132237

$endgroup$

add a comment | 

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3147614%2fex-neq-0-proof-correctness%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

7

$begingroup$

The proof is not correct because it assumes implicitely that if a sequence $(a_n)_ninmathbb N$ converges to $1$, then $lim_ntoinftya_n^n=1$. This is not true. For instance,$$lim_ntoinfty left (1 + frac1n right )=1text and lim_ntoinftyleft(1 + frac1nright)^n=eneq1.$$

share|cite|improve this answer

edited Mar 14 at 6:22

Dbchatto67

1,995319

answered Mar 14 at 6:16

José Carlos SantosJosé Carlos Santos

169k23132237

$endgroup$

add a comment | 

7

$begingroup$

The proof is not correct because it assumes implicitely that if a sequence $(a_n)_ninmathbb N$ converges to $1$, then $lim_ntoinftya_n^n=1$. This is not true. For instance,$$lim_ntoinfty left (1 + frac1n right )=1text and lim_ntoinftyleft(1 + frac1nright)^n=eneq1.$$

share|cite|improve this answer

edited Mar 14 at 6:22

Dbchatto67

1,995319

answered Mar 14 at 6:16

José Carlos SantosJosé Carlos Santos

169k23132237

$endgroup$

add a comment | 

$begingroup$

The proof is not correct because it assumes implicitely that if a sequence $(a_n)_ninmathbb N$ converges to $1$, then $lim_ntoinftya_n^n=1$. This is not true. For instance,$$lim_ntoinfty left (1 + frac1n right )=1text and lim_ntoinftyleft(1 + frac1nright)^n=eneq1.$$

share|cite|improve this answer

edited Mar 14 at 6:22

Dbchatto67

1,995319

answered Mar 14 at 6:16

José Carlos SantosJosé Carlos Santos

169k23132237

$endgroup$

share|cite|improve this answer

edited Mar 14 at 6:22

Dbchatto67

1,995319

answered Mar 14 at 6:16

José Carlos SantosJosé Carlos Santos

169k23132237

edited Mar 14 at 6:22

Dbchatto67

1,995319

edited Mar 14 at 6:22

Dbchatto67

1,995319

answered Mar 14 at 6:16

José Carlos SantosJosé Carlos Santos

169k23132237

answered Mar 14 at 6:16

José Carlos SantosJosé Carlos Santos

169k23132237