Hfrhyu

Extremely, Sorry about the vertical upload or the capture of the scale, Could you please consider the picture as horizontal, I need to draw this, I am able to learn from here the following: But I need to re-draw this in my current situation: Will be grateful for the help. Between 1 and k, dot dot will be fine instead of small line segments which I have drawn for P or t.

documentclass[tikz,border=3.14mm]standalone
begindocument
begintikzpicture
 pgfmathtruncatemacroL10 %<- length of the line
 pgfmathtruncatemacrokmax6 
 pgfmathtruncatemacrotmax7
 draw (0,0) -- (L,0);
 foreach k in 0,...,kmax
 draw (L*k/kmax,0.2) -- (L*k/kmax,-0.2) ifnumk<2 node[below,text
 height=1.5ex]$k$fi
 ifnumk=numexprkmax-1 node[below,text
 height=1.5ex]$k$fi
 ifnumk=kmax node[below,text
 height=1.5ex]$k+1$fi;
 ifnumk<kmax
 foreach t in 1,2,...,tmax
 draw (L*k/kmax+L*(t/(tmax+1))/kmax,-0.1) 
 -- (L*k/kmax+L*(t/(tmax+1))/kmax,0.1)
 node[above] $ifnumt=tmax
 telseifnumt<4
 telse .fifi$ ;
 fi
endtikzpicture
enddocument 

I also learned these today:

begintikzpicture[xscale=8]
draw[-][draw=red, very thick] (0,0) -- (.5,0);
draw[-][draw=green, very thick] (.5,0) -- (1,0);
draw [thick] (0,-.1) node[below]0 -- (0,0.1);
draw [thick] (0.5,-.1) node[below]$a=b=1/2$ -- (0.5,0.1);
draw [thick] (1,-.1) node[below]1 -- (1,0.1);
endtikzpicture


draw[-][draw=red, very thick] (0,0) -- (.5,0);
draw[-][draw=green, very thick] (.5,0) -- (1,0);
draw [thick] (0,-.1) node[below]0 -- (0,0.1);
0
draw [thick] (0.5,-.1) node[below]$a=b=1/2$ -- (0.5,0.1);
0 a = b = 1/2
draw [thick] (1,-.1) node[below]1 -- (1,0.1);

You need not such a complicated code.

documentclass[tikz]standalone
begindocument
begintikzpicture[x=0.8cm]
draw[-latex] (0,0) -- (21,0);
foreach i [count=j] in 0,5,10
 draw (i,0) -- (i,-.2) node[below,align=center] j\$P_j$;
draw (12,0) -- (12,-.2) node[below,align=center] $k$\$P_k$;
draw (17,0) -- (17,-.2) node[below,align=center] $k+1$\$P_k+1$;
foreach i [count=j from 0] in 1,6 
 draw (i,0) -- (i,.2) node[above,align=center] $a_j$\1;
 draw (i+1,0) -- (i+1,.2) node[above,align=center] $a_j$\2;
 path (i+2,.2) node[above] $ldots$;
 draw (i+3,0) -- (i+3,.2) node[above,align=center] $a_j$\$t$;

draw (13,0) -- (13,.2) node[above,align=center] $a_k$\1;
draw (14,0) -- (14,.2) node[above,align=center] $a_k$\2;
path (15,.2) node[above] $ldots$;
draw (16,0) -- (16,.2) node[above,align=center] $a_k$\$t$;
draw (18,0) -- (18,.2) node[above,align=center] $a_k+1$\1;
draw (19,0) -- (19,.2) node[above,align=center] $a_k+1$\2;
path (20,.2) node[above] $ldots$;
path (11,-.2) node[below] $ldots$;
path (11,.2) node[above] $ldots$;
endtikzpicture
enddocument

(open the image in a new tab for better resolution)

Something like this??

documentclass[tikz,border=3.14mm]standalone
usepackagestackengine
renewcommandstacktypeL
stackMath
begindocument
begintikzpicture
 pgfmathtruncatemacroL20 %<- length of the line
 pgfmathtruncatemacrokmax6 
 pgfmathtruncatemacrotmax7
 draw (0,0) -- (L,0);
 foreach k in 0,...,kmax
 draw (L*k/kmax,0.2) -- (L*k/kmax,-0.2) ifnumk<2 node[below,text
 height=1.5ex]$k$fi
 ifnumk=numexprkmax-1 node[below,text
 height=1.5ex]$k$fi
 ifnumk=kmax node[below,text
 height=1.5ex]$k+1$fi;
 ifnumk<kmax
 foreach t in 1,2,...,tmax
 draw (L*k/kmax+L*(t/(tmax+1))/kmax,-0.1) 
 -- (L*k/kmax+L*(t/(tmax+1))/kmax,0.1)
 node[above] $ifnumt=tmax
 ifnumk=5relaxdefqkelsedefqkfi
 stackonta_q^telseifnumt<4
 ifnumk=5relaxdefqkelsedefqkfi
 stackonta_q^telse .fifi$ ;
 fi
endtikzpicture
enddocument 

Zoom near k: