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The code below does not work. Can anyone tell me why? Thanks!

 For[t = -1, t <= 1, t = t + 0.01, 
 For[z = -1, z <= 1, z = z + 0.01, If[t*z == 0, Print[t, ", ", z]]]]
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1 Answer 1

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It's the result of error accumulation of float number:

Nest[# + 0.01 &, -1, 100]
% == 0
(* 7.5287*10^-16 *)
(* False *)

There're many ways to fix this, for example, using arbitrary-precision number. In your case a Precision of 1. is enough:

0.01`1 // Precision
Nest[# + 0.01`1 &, -1, 100]
% == 0
(* 1. *)
(* 0.*10^-1 *)
(* True *)

Or simply use exact number:

Nest[# + 1/100 &, -1, 100]
% == 0
(* 0 *)
(* True *)
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  • $\begingroup$ What if I have a function gives numerical values, for example, if I have something like f(0.01,0.02)=0.2312, and I want to check if f(a,b)==0, how should I do this? $\endgroup$
    – lol
    Jul 4, 2016 at 18:19
  • $\begingroup$ @lol This depends on the structure of the function $\endgroup$
    – xzczd
    Jul 5, 2016 at 2:25

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