For loop continue going after reaching goal. Delphi - delphi

Question

This issue appears only with numbers, bigger, then 12 including.
Those two pictures captured in one time. How it is even possible?
For loop must go from 0 to 12-1=11, doesn't it?
Nevertheless, when I use while loop instead, it works fine.
Is it my fault or Delphi's?
P.S. Code down bellow.
unit Unit1;
interface
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, StdCtrls, Grids;
type
TForm1 = class(TForm)
StringGrid1: TStringGrid;
Button1: TButton;
Edit1: TEdit;
Button2: TButton;
Label1: TLabel;
Button3: TButton;
Label2: TLabel;
Label3: TLabel;
procedure Button1Click(Sender: TObject);
procedure Button2Click(Sender: TObject);
procedure StringGrid1KeyPress(Sender: TObject; var Key: Char);
procedure Button3Click(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;
var
Form1: TForm1;
n:Integer;
implementation
{$R *.dfm}
procedure TForm1.Button1Click(Sender: TObject); //Button, that sets array length
var
i, index:Integer;
begin
val(Edit1.Text, n, index);
if(index<>0) then
begin
ShowMessage('Wrong number');
Edit1.Clear();
exit;
end;
StringGrid1.ColCount:=n;
for i:=0 to n-1 do
StringGrid1.Cells[i,0]:=IntToStr(i+1);
StringGrid1.SetFocus();
end;
procedure TForm1.Button2Click(Sender: TObject); //Main button
var
i, index:Integer;
a:array[0..10] of Real;
denom, sum:Real;
begin
i:=0;
sum:=0;
denom:=-1;
//that for loop from screenshot is here
for i:=0 to n-1 do
//while i<=(n-1) do
begin
Val(StringGrid1.cells[i,1], a[i], index);
if(index<>0) then
begin
ShowMessage('Wrong number with ' + IntToStr(i+1) + ' Id');
StringGrid1.Col:=i;
StringGrid1.Row:=1;
StringGrid1.SetFocus();
exit;
end;
a[i]:=a[i]/denom;
sum:=sum+a[i];
StringGrid1.Cells[i,2]:=FloatToStrF(a[i],ffFixed,5,3);
denom:=-denom*(i+2);
//Inc(i);
end;
Label2.Caption:=FloatToStrF(sum,ffFixed,5,3);
end;
//code down bellow just allow to go to another cell by pressing Enter
procedure TForm1.StringGrid1KeyPress(Sender: TObject; var Key: Char);
begin
if (Key=#13) and (StringGrid1.Col=(n-1)) then
Button2.SetFocus()
else if (Key=#13) and (StringGrid1.Col<>(n-1)) then
StringGrid1.Col:=StringGrid1.Col+1;
end;
procedure TForm1.Button3Click(Sender: TObject);
begin
Close();
end;
end.

Answer 1

As to answer your question of 'how is this even possible'...
In your screen, n is 12. As pointed out by Kermation, the highest index of a is 10, so when i is 11, unless you have range checking activated, when you write to a[11] (i=11) you will overwrite something else. This is in the local variable area so it might be i, for instance, or even internal variables you can't see like the limit used for the for loop, which is calculated at the start of the loop. Once you allow this to happen, pretty much anything is possible.
Of course the exact manifestation of the problem will very from one version of the compiler to another. In one version you might get away with it. in another you won't.

Answer 2

Array a size was smaller, then amount of cells.