# \[?\] Is there one term missing when using Table? **URL:** \ **Category:** Questions\ **Tags:** algebra, calculus\ **Created:** [October 22, 2017, 10:46pm UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419 "2017-10-22T22:46:17Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![gouwangzhangdong](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/gouwangzhangdong/32/34499_2.png) [@gouwangzhangdong](https://community.wolfram.com/u/gouwangzhangdong)\ **Post date:** [October 22, 2017, 10:46pm UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419/1 "2017-10-22T22:46:17Z")
Hey guys: When I use “Table” to get a series calculation results for A from 0 to 1 with gap 0.1. So there should be 11 elements in the list at last while “Table” only gives me 10 results and miss the last one when A=1. Really appreciate someone can tell me what happened and how to improve this. You may also find the commands in the attachment. ``` $PreRead = (# /. s_String /; StringMatchQ[s, NumberString] && Precision@ToExpression@s == MachinePrecision :> s <> "`50." &); skew[A_, \[Alpha]_, \[Beta]_, \[Delta]_] = (2 Sqrt[\[Delta]] (((-1 + A) A (\[Alpha] - \[Beta])^2 (A^2 (\[Alpha] - \[Beta])^2 - A (\[Alpha] - \[Beta]) (\[Alpha] - \[Beta] - \[Delta]) + \ \[Beta] (\[Alpha] + \[Delta])) (-(-1 + A) \[Beta] \[Delta] + \[Alpha] (\[Beta] + A \[Delta])))/(((-1 + A) \[Alpha] - A \[Beta] - 3 \[Delta]) ((-1 + A) \[Alpha] - A \[Beta] - 2 \[Delta]) (\[Alpha] - A \[Alpha] + A \[Beta] + \[Delta])^3) + (-3 (-1 + A) \[Beta] \[Delta] + \[Alpha] (\[Beta] + 3 A \[Delta]))/(\[Alpha] - A \[Alpha] + A \[Beta] + 3 \[Delta]) - ((-1 + A) A (\[Alpha] - \[Beta])^2 (-3 (-1 + A) \[Beta] \[Delta] + \[Alpha] (2 \[Beta] + 3 A \[Delta])))/((\[Alpha] - A \[Alpha] + A \[Beta] + \[Delta]) (\[Alpha] - A \[Alpha] + A \[Beta] + 2 \[Delta]) (\[Alpha] - A \[Alpha] + A \[Beta] + 3 \[Delta]))))/(((-1 + A) A (\[Alpha] - \[Beta])^2 (-(-1 + A) \[Beta] \[Delta] + \[Alpha] (\[Beta] + A \[Delta])))/(((-1 + A) \[Alpha] - A \[Beta] - 2 \[Delta]) (\[Alpha] - A \[Alpha] + A \[Beta] + \[Delta])^2) + (-2 (-1 + A) \[Beta] \[Delta] + \[Alpha] (\[Beta] + 2 A \[Delta]))/(\[Alpha] - A \[Alpha] + A \[Beta] + 2 \[Delta]))^(3/2); Table[skew[A, 20.1, 2.98, 0.015], {A, 0, 1, 0.1}] // N Length[%] {0.141895, 0.139203, 0.135927, 0.131859, 0.126677, 0.11985, 0.110442, \ 0.0966346, 0.0744006, 0.033185} 10 ``` Thanks in advance ---
**Author:** ![bsimpson141421356](https://avatars.discourse-cdn.com/v4/letter/b/ac91a4/32.png) [@bsimpson141421356](https://community.wolfram.com/u/bsimpson141421356)\ **Post date:** [October 23, 2017, 6:06am UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419/2 "2017-10-23T06:06:45Z")
Hint ``` In[1]:= ... Length[Table[skew[A, 20.1, 2.98, 0.015], {A, 0, 1, 0.1}]] Out[3]= 10 ``` versus ``` In[1]:= ... Length[Table[skew[A, 20.1, 2.98, 0.015], {A, 0, 1, 1/10}]] Out[3]= 11 ``` ---
**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\ **Post date:** [October 23, 2017, 6:42am UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419/3 "2017-10-23T06:42:59Z")
Perhaps it’s because if you sum ten instances of .1`50. you get someting slightly more than 1: ``` In[2]:= .1`50. + .1`50. + .1`50. + .1`50. + .1`50. + .1`50. + .1`50. \ + .1`50. + .1`50. + .1`50. // FullForm Out[2] 1.0000000000000000000000000000000000000000000000000000000000000000000000\ 0000003`50. ``` ---
**Author:** ![gouwangzhangdong](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/gouwangzhangdong/32/34499_2.png) [@gouwangzhangdong](https://community.wolfram.com/u/gouwangzhangdong)\ **Post date:** [October 23, 2017, 8:20am UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419/4 "2017-10-23T08:20:34Z")
Sorry, I still do not what is happening here. I set up a table for k from 1 to 2 with gap 0.1. It turns out that the results are the same no matter gap being 0.1 or 1/10. Please see more details in the attachment. ---
**Author:** ![sghuisman](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sghuisman/32/27850_2.png) [@sghuisman](https://community.wolfram.com/u/sghuisman)\ **Post date:** [October 23, 2017, 8:31am UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419/5 "2017-10-23T08:31:04Z")
0.1 is never really 0.1 in binary representation: ``` Table[A, {A, 0, 1, 0.1`50}] ``` if you copy the last number you will see: ``` 0.90000000000000000000000000000000000000000000000000000000000000000000000000003`50. ``` i.e. a little bit more than 0.9, use exact arithmetic to be sure it is 11, or use Subdivide: ``` Table[A, {A, Subdivide[0, 1, 10]}] ``` ---
**Author:** ![jasondbiggs](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/jasondbiggs/32/28365_2.png) [@jasondbiggs](https://community.wolfram.com/u/jasondbiggs)\ **Post date:** [October 23, 2017, 8:13pm UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419/6 "2017-10-23T20:13:27Z")
Just to clarify, this is the normal behavior ```auto In[7]:= Length@Table[x, {x, 0, 1, .1}] Out[7]= 11 ``` When you do something drastic like ```auto $PreRead = (# /. s_String /; StringMatchQ[s, NumberString] && Precision@ToExpression@s == MachinePrecision :> s <> "`50." &); ``` then you need to be ready for the consequences, among which is ```auto In[10]:= Length@Table[x, {x, 0, 1, .1}] Out[10]= 10 ``` Since you want your answers to such a high number of digits, why not just keep everything as rational and use `N` at the end? ```auto skew[Amp_, ?mp_, ?mp_, ?mp_] := Module[{A = Rationalize@Amp, ? = Rationalize@?mp, ? = Rationalize@?mp, ? = Rationalize@?mp}, (2 Sqrt[?] (((-1 + A) A (? - ?)^2 (A^2 (? - ?)^2 - A (? - ?) (? - ? - ?) \ + ? (? + ?)) (-(-1 + A) ? ? + ? (? + A ?)))/(((-1 + A) ? - A ? - 3 ?) ((-1 + A) ? - A ? - 2 ?) (? - A ? + A ? + ?)^3) + (-3 (-1 + A) ? ? + ? (? + 3 A ?))/(? - A ? + A ? + 3 ?) - ((-1 + A) A (? - ?)^2 (-3 (-1 + A) ? ? + ? (2 ? + 3 A ?)))/((? - A ? + A ? + ?) (? - A ? + A ? + 2 ?) (? - A ? + A ? + 3 ?))))/(((-1 + A) A (? - ?)^2 (-(-1 + A) ? ? + ? (? + A ?)))/(((-1 + A) ? - A ? - 2 ?) (? - A ? + A ? + ?)^2) + (-2 (-1 + A) ? ? + ? (? + 2 A ?))/(? - A ? + A ? + 2 ?))^(3/2) ]; In[2]:= Table[skew[A, 20.1, 2.98, 0.015], {A, 0, 1, 0.1}] // N[#, 50] & Length[%] Out[2]= {0.14189513095212063367049531962987546141568326643434, \ 0.13920344101328578263969756404215809382766534147239, \ 0.13592716321563841983794812006874993948237693570027, \ 0.13185917327785972103954298320739470452252943280392, \ 0.12667686295955584799447506972227890015016781166517, \ 0.11984973711991386295060361312735642563028850992476, \ 0.11044152395284289944251345711595700385738865557709, \ 0.096634643366104288816678293713331415198513960340867, \ 0.074400586745371447280910852144971096789513221053062, \ 0.033185045336993739355804248832880796377132424223379, \ 0.054635836470815303531952862734950163493012524454082} Out[3]= 11 ``` ---
**Author:** ![gouwangzhangdong](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/gouwangzhangdong/32/34499_2.png) [@gouwangzhangdong](https://community.wolfram.com/u/gouwangzhangdong)\ **Post date:** [October 23, 2017, 9:56pm UTC](https://community.wolfram.com/t/is-there-one-term-missing-when-using-table/11419/7 "2017-10-23T21:56:08Z")
Thank you guys. Your comments answered my question well and I have learned a lot.