What's wrong with this bogus proof?
$begingroup$
What is the mistake here? Is it matter of the unit?
discrete-mathematics proof-verification
$endgroup$
add a comment |
$begingroup$
What is the mistake here? Is it matter of the unit?
discrete-mathematics proof-verification
$endgroup$
5
$begingroup$
Yes, the units don’t match across the 2nd equals sign
$endgroup$
– Alex
4 hours ago
2
$begingroup$
Yes, you have to square the unit. Conversion of squared units is different: if 100 cents is a dollar, then $100^2$ cents squared is a dollar squred.
$endgroup$
– Dean Young
4 hours ago
add a comment |
$begingroup$
What is the mistake here? Is it matter of the unit?
discrete-mathematics proof-verification
$endgroup$
What is the mistake here? Is it matter of the unit?
discrete-mathematics proof-verification
discrete-mathematics proof-verification
asked 4 hours ago
ShinobuIsMyWifeShinobuIsMyWife
413
413
5
$begingroup$
Yes, the units don’t match across the 2nd equals sign
$endgroup$
– Alex
4 hours ago
2
$begingroup$
Yes, you have to square the unit. Conversion of squared units is different: if 100 cents is a dollar, then $100^2$ cents squared is a dollar squred.
$endgroup$
– Dean Young
4 hours ago
add a comment |
5
$begingroup$
Yes, the units don’t match across the 2nd equals sign
$endgroup$
– Alex
4 hours ago
2
$begingroup$
Yes, you have to square the unit. Conversion of squared units is different: if 100 cents is a dollar, then $100^2$ cents squared is a dollar squred.
$endgroup$
– Dean Young
4 hours ago
5
5
$begingroup$
Yes, the units don’t match across the 2nd equals sign
$endgroup$
– Alex
4 hours ago
$begingroup$
Yes, the units don’t match across the 2nd equals sign
$endgroup$
– Alex
4 hours ago
2
2
$begingroup$
Yes, you have to square the unit. Conversion of squared units is different: if 100 cents is a dollar, then $100^2$ cents squared is a dollar squred.
$endgroup$
– Dean Young
4 hours ago
$begingroup$
Yes, you have to square the unit. Conversion of squared units is different: if 100 cents is a dollar, then $100^2$ cents squared is a dollar squred.
$endgroup$
– Dean Young
4 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
$$0.01=(sqrt{$}0.1)^2$, not $($0.1)^2$.
$endgroup$
add a comment |
$begingroup$
You can clearly see the fallacy if you keep track of the units:
In the second equality, $$0.01 = $0.1times $0.1$ is not true, if you are doing units.
Even if the second equality were true, the third one gives problems: since $c=$/100$, you have
$$
($0.1)^2=left(frac c{100},0.1right)^2=frac{c^2}{100}timesfrac1{10}=frac{c^2}{1000}.
$$
This is not $(10c)^2=100c^2$.
In conclusion, two equalities are bogus, and so is the argument.
$endgroup$
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
});
}
});
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3144460%2fwhats-wrong-with-this-bogus-proof%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$0.01=(sqrt{$}0.1)^2$, not $($0.1)^2$.
$endgroup$
add a comment |
$begingroup$
$$0.01=(sqrt{$}0.1)^2$, not $($0.1)^2$.
$endgroup$
add a comment |
$begingroup$
$$0.01=(sqrt{$}0.1)^2$, not $($0.1)^2$.
$endgroup$
$$0.01=(sqrt{$}0.1)^2$, not $($0.1)^2$.
answered 4 hours ago
ArthurArthur
117k7116200
117k7116200
add a comment |
add a comment |
$begingroup$
You can clearly see the fallacy if you keep track of the units:
In the second equality, $$0.01 = $0.1times $0.1$ is not true, if you are doing units.
Even if the second equality were true, the third one gives problems: since $c=$/100$, you have
$$
($0.1)^2=left(frac c{100},0.1right)^2=frac{c^2}{100}timesfrac1{10}=frac{c^2}{1000}.
$$
This is not $(10c)^2=100c^2$.
In conclusion, two equalities are bogus, and so is the argument.
$endgroup$
add a comment |
$begingroup$
You can clearly see the fallacy if you keep track of the units:
In the second equality, $$0.01 = $0.1times $0.1$ is not true, if you are doing units.
Even if the second equality were true, the third one gives problems: since $c=$/100$, you have
$$
($0.1)^2=left(frac c{100},0.1right)^2=frac{c^2}{100}timesfrac1{10}=frac{c^2}{1000}.
$$
This is not $(10c)^2=100c^2$.
In conclusion, two equalities are bogus, and so is the argument.
$endgroup$
add a comment |
$begingroup$
You can clearly see the fallacy if you keep track of the units:
In the second equality, $$0.01 = $0.1times $0.1$ is not true, if you are doing units.
Even if the second equality were true, the third one gives problems: since $c=$/100$, you have
$$
($0.1)^2=left(frac c{100},0.1right)^2=frac{c^2}{100}timesfrac1{10}=frac{c^2}{1000}.
$$
This is not $(10c)^2=100c^2$.
In conclusion, two equalities are bogus, and so is the argument.
$endgroup$
You can clearly see the fallacy if you keep track of the units:
In the second equality, $$0.01 = $0.1times $0.1$ is not true, if you are doing units.
Even if the second equality were true, the third one gives problems: since $c=$/100$, you have
$$
($0.1)^2=left(frac c{100},0.1right)^2=frac{c^2}{100}timesfrac1{10}=frac{c^2}{1000}.
$$
This is not $(10c)^2=100c^2$.
In conclusion, two equalities are bogus, and so is the argument.
edited 3 hours ago
J. W. Tanner
3,1081320
3,1081320
answered 4 hours ago
Martin ArgeramiMartin Argerami
128k1184184
128k1184184
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3144460%2fwhats-wrong-with-this-bogus-proof%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
5
$begingroup$
Yes, the units don’t match across the 2nd equals sign
$endgroup$
– Alex
4 hours ago
2
$begingroup$
Yes, you have to square the unit. Conversion of squared units is different: if 100 cents is a dollar, then $100^2$ cents squared is a dollar squred.
$endgroup$
– Dean Young
4 hours ago