eruvin 82

They were sitting opposite from me on the tube. It looked like a half-term shopping trip for teenage daughter and mum. She closed her eyes and fitted herself around her mother's body and held on. Every so often she took a sip from her mother's water bottle. Neither said a word to each other the whole journey. Just tenderly travelling together.

and yet the Sages asked "who is the child who does not need their mother? what age? 4 or 5, or 6....?"

but there seems to be no age limit. No tachum.

(this page discusses that a child is included in their mother's eruv and shabbat boundaries up until they no longer need their mother. The shabbat boundary called the tachum, and is the limit one is permitted to walk on shabbat)

eruvin 38

some ropes are used to bind and restrict. to hold down the red heifer, to hold up the sotah's clothing.

and some ropes are used to measure, to allow freedom of movement.

(measuring the shabbat boundary should be done with a 50 cubit rope made of plant material. not iron chains, even though they would not stretch. other ropes are mentioned, each with their own uses. some ropes used to tie down and restrict, but the shabbat boundary is there is allow for movement and therefore there is room for leniency)