Why is (1-t)^2 == (t-1)^2 in SageMath?
-1
$begingroup$
This is really odd, not much to say about it.
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.5, Release Date: 2018-12-22 │
│ Using Python 2.7.15. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sagemath
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
$endgroup$
add a comment |
-1
$begingroup$
This is really odd, not much to say about it.
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.5, Release Date: 2018-12-22 │
│ Using Python 2.7.15. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sagemath
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
$endgroup$
$begingroup$
Are you sure this question wouldn't be better answered in another SE?
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:06
$begingroup$
@AniruddhVenkatesan Where would you recommend?
$endgroup$
– Louis Hong
Jan 19 at 4:07
$begingroup$
That depends on what type of answer you're looking for. If you're looking for a reason as to why Python respond and return this result, Stack Overflow might be a better choice. If you want a mathematical explanation, then I would suggest leaving the question on this site and trying to see if someone knows the answer
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:11
3
$begingroup$
What is "odd" about this? Do you have reason to doubt the result? What result did you expect and why?
$endgroup$
– JMoravitz
Jan 19 at 4:15
add a comment |
-1
-1
-1
$begingroup$
This is really odd, not much to say about it.
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.5, Release Date: 2018-12-22 │
│ Using Python 2.7.15. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sagemath
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
$endgroup$
This is really odd, not much to say about it.
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.5, Release Date: 2018-12-22 │
│ Using Python 2.7.15. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sagemath
sagemath
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
asked Jan 19 at 4:03
Louis HongLouis Hong
1197
1197
$begingroup$
Are you sure this question wouldn't be better answered in another SE?
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:06
$begingroup$
@AniruddhVenkatesan Where would you recommend?
$endgroup$
– Louis Hong
Jan 19 at 4:07
$begingroup$
That depends on what type of answer you're looking for. If you're looking for a reason as to why Python respond and return this result, Stack Overflow might be a better choice. If you want a mathematical explanation, then I would suggest leaving the question on this site and trying to see if someone knows the answer
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:11
3
$begingroup$
What is "odd" about this? Do you have reason to doubt the result? What result did you expect and why?
$endgroup$
– JMoravitz
Jan 19 at 4:15
add a comment |
$begingroup$
Are you sure this question wouldn't be better answered in another SE?
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:06
$begingroup$
@AniruddhVenkatesan Where would you recommend?
$endgroup$
– Louis Hong
Jan 19 at 4:07
$begingroup$
That depends on what type of answer you're looking for. If you're looking for a reason as to why Python respond and return this result, Stack Overflow might be a better choice. If you want a mathematical explanation, then I would suggest leaving the question on this site and trying to see if someone knows the answer
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:11
3
$begingroup$
What is "odd" about this? Do you have reason to doubt the result? What result did you expect and why?
$endgroup$
– JMoravitz
Jan 19 at 4:15
$begingroup$
Are you sure this question wouldn't be better answered in another SE?
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:06
$begingroup$
Are you sure this question wouldn't be better answered in another SE?
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:06
$begingroup$
@AniruddhVenkatesan Where would you recommend?
$endgroup$
– Louis Hong
Jan 19 at 4:07
$begingroup$
@AniruddhVenkatesan Where would you recommend?
$endgroup$
– Louis Hong
Jan 19 at 4:07
$begingroup$
That depends on what type of answer you're looking for. If you're looking for a reason as to why Python respond and return this result, Stack Overflow might be a better choice. If you want a mathematical explanation, then I would suggest leaving the question on this site and trying to see if someone knows the answer
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:11
$begingroup$
That depends on what type of answer you're looking for. If you're looking for a reason as to why Python respond and return this result, Stack Overflow might be a better choice. If you want a mathematical explanation, then I would suggest leaving the question on this site and trying to see if someone knows the answer
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:11
3
3
$begingroup$
What is "odd" about this? Do you have reason to doubt the result? What result did you expect and why?
$endgroup$
– JMoravitz
Jan 19 at 4:15
$begingroup$
What is "odd" about this? Do you have reason to doubt the result? What result did you expect and why?
$endgroup$
– JMoravitz
Jan 19 at 4:15
add a comment |
2 Answers
2
active
oldest
votes
2
$begingroup$
This is just basic algebra, namely laws of exponents:
$(t-1)^2 = (-1(1-t))^2= (-1)^2(1-t)^2 = (1-t)^2$
answered Jan 19 at 4:11
RandallRandall
10.8k11431
$endgroup$
2
$begingroup$
should have paid attention in elementary school
$endgroup$
– Louis Hong
Jan 19 at 4:16
1
$begingroup$
To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah.
$endgroup$
– Randall
Jan 19 at 4:16
add a comment |
1
$begingroup$
Forget $1-t$. Instead, think $T$. Is it so surprising/odd that $$(T)^2 = (-T)^2$$
?
Alternatively we can expand them:
$$(1-t)(1-t)=(1)(1) +(2)(1)(-t)+(-t)(-t)=1-2t+t^2$$
$$(t-1)(t-1)=(t)(t)+2(-1)(t)+(-1)(-1)=t^2-2t+1$$
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
2
$begingroup$
This is just basic algebra, namely laws of exponents:
$(t-1)^2 = (-1(1-t))^2= (-1)^2(1-t)^2 = (1-t)^2$
answered Jan 19 at 4:11
RandallRandall
10.8k11431
$endgroup$
2
$begingroup$
should have paid attention in elementary school
$endgroup$
– Louis Hong
Jan 19 at 4:16
1
$begingroup$
To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah.
$endgroup$
– Randall
Jan 19 at 4:16
add a comment |
2
$begingroup$
This is just basic algebra, namely laws of exponents:
$(t-1)^2 = (-1(1-t))^2= (-1)^2(1-t)^2 = (1-t)^2$
answered Jan 19 at 4:11
RandallRandall
10.8k11431
$endgroup$
2
$begingroup$
should have paid attention in elementary school
$endgroup$
– Louis Hong
Jan 19 at 4:16
1
$begingroup$
To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah.
$endgroup$
– Randall
Jan 19 at 4:16
add a comment |
2
2
2
$begingroup$
This is just basic algebra, namely laws of exponents:
$(t-1)^2 = (-1(1-t))^2= (-1)^2(1-t)^2 = (1-t)^2$
answered Jan 19 at 4:11
RandallRandall
10.8k11431
$endgroup$
This is just basic algebra, namely laws of exponents:
$(t-1)^2 = (-1(1-t))^2= (-1)^2(1-t)^2 = (1-t)^2$
answered Jan 19 at 4:11
RandallRandall
10.8k11431
answered Jan 19 at 4:11
RandallRandall
10.8k11431
answered Jan 19 at 4:11
RandallRandall
10.8k11431
answered Jan 19 at 4:11
RandallRandall
10.8k11431
10.8k11431
2
$begingroup$
should have paid attention in elementary school
$endgroup$
– Louis Hong
Jan 19 at 4:16
1
$begingroup$
To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah.
$endgroup$
– Randall
Jan 19 at 4:16
add a comment |
2
$begingroup$
should have paid attention in elementary school
$endgroup$
– Louis Hong
Jan 19 at 4:16
1
$begingroup$
To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah.
$endgroup$
– Randall
Jan 19 at 4:16
2
2
$begingroup$
should have paid attention in elementary school
$endgroup$
– Louis Hong
Jan 19 at 4:16
$begingroup$
should have paid attention in elementary school
$endgroup$
– Louis Hong
Jan 19 at 4:16
1
1
$begingroup$
To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah.
$endgroup$
– Randall
Jan 19 at 4:16
$begingroup$
To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah.
$endgroup$
– Randall
Jan 19 at 4:16
add a comment |
1
$begingroup$
Forget $1-t$. Instead, think $T$. Is it so surprising/odd that $$(T)^2 = (-T)^2$$
?
Alternatively we can expand them:
$$(1-t)(1-t)=(1)(1) +(2)(1)(-t)+(-t)(-t)=1-2t+t^2$$
$$(t-1)(t-1)=(t)(t)+2(-1)(t)+(-1)(-1)=t^2-2t+1$$
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
$endgroup$
add a comment |
1
$begingroup$
Forget $1-t$. Instead, think $T$. Is it so surprising/odd that $$(T)^2 = (-T)^2$$
?
Alternatively we can expand them:
$$(1-t)(1-t)=(1)(1) +(2)(1)(-t)+(-t)(-t)=1-2t+t^2$$
$$(t-1)(t-1)=(t)(t)+2(-1)(t)+(-1)(-1)=t^2-2t+1$$
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
$endgroup$
add a comment |
1
1
1
$begingroup$
Forget $1-t$. Instead, think $T$. Is it so surprising/odd that $$(T)^2 = (-T)^2$$
?
Alternatively we can expand them:
$$(1-t)(1-t)=(1)(1) +(2)(1)(-t)+(-t)(-t)=1-2t+t^2$$
$$(t-1)(t-1)=(t)(t)+2(-1)(t)+(-1)(-1)=t^2-2t+1$$
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
$endgroup$
Forget $1-t$. Instead, think $T$. Is it so surprising/odd that $$(T)^2 = (-T)^2$$
?
Alternatively we can expand them:
$$(1-t)(1-t)=(1)(1) +(2)(1)(-t)+(-t)(-t)=1-2t+t^2$$
$$(t-1)(t-1)=(t)(t)+2(-1)(t)+(-1)(-1)=t^2-2t+1$$
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
answered Jan 19 at 4:40
Rhys HughesRhys Hughes
7,1051630
7,1051630
add a comment |
add a comment |
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$begingroup$
Are you sure this question wouldn't be better answered in another SE?
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:06
$begingroup$
@AniruddhVenkatesan Where would you recommend?
$endgroup$
– Louis Hong
Jan 19 at 4:07
$begingroup$
That depends on what type of answer you're looking for. If you're looking for a reason as to why Python respond and return this result, Stack Overflow might be a better choice. If you want a mathematical explanation, then I would suggest leaving the question on this site and trying to see if someone knows the answer
$endgroup$
– Aniruddh Venkatesan
Jan 19 at 4:11
3
$begingroup$
What is "odd" about this? Do you have reason to doubt the result? What result did you expect and why?
$endgroup$
– JMoravitz
Jan 19 at 4:15