SECONDS variable not shown from set, not updated properly

[Wayne Pollock]

Configuration Information [Automatically generated, do not change]:
Machine: i686
OS: linux-gnu
Compiler: gcc
Compilation CFLAGS:  -DPROGRAM='bash' -DCONF_HOSTTYPE='i686'
-DCONF_OSTYPE='linux-gnu'
-DCONF_MACHTYPE='i686-pc-linux-gnu' -DCONF_VENDOR='pc' -DSHELL
-DHAVE_CONFIG_H
-D_GNU_SOURCE  -I.  -I. -I./include -I./lib -O2 -march=i386 -mcpu=i686
uname output: Linux YborStudent 2.4.20-13.7 #1 Mon May 12 13:13:52 EDT
2003 i686
unknown
Machine Type: i686-pc-linux-gnu

Bash Version: 2.05a
Patch Level: 0
Release Status: release

Description:
        SECONDS doesn't initially show in the output of the set
        command.  It only shows up after $SECONDS has been referenced,
        and even then is not updated in that output.

Repeat-By:
        $ set |grep SEC
        $ echo $SECONDS
        20
        $ set |grep SEC
        SECONDS=20
        $ sleep 10
        $ set |grep SEC
        SECONDS=20
        $ echo $SECONDS
        45
        $ set |grep SEC
        SECONDS=45
        $