Question

be definition of cantor set, what is the normal closed intervals length in cantor set ?​

Answer 1

ɪɴ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs, ᴛʜᴇ ᴄᴀɴᴛᴏʀ sᴇᴛ ɪs ᴀ sᴇᴛ ᴏғ ᴘᴏɪɴᴛs ʟʏɪɴɢ ᴏɴ ᴀ sɪɴɢʟᴇ ʟɪɴᴇ sᴇɢᴍᴇɴᴛ ᴛʜᴀᴛ ʜᴀs ᴀ ɴᴜᴍʙᴇʀ ᴏғ ʀᴇᴍᴀʀᴋᴀʙʟᴇ ᴀɴᴅ ᴅᴇᴇᴘ ᴘʀᴏᴘᴇʀᴛɪᴇs. ɪᴛ ᴡᴀs ᴅɪsᴄᴏᴠᴇʀᴇᴅ ɪɴ ʙʏ ʜᴇɴʀʏ ᴊᴏʜɴ sᴛᴇᴘʜᴇɴ sᴍɪᴛʜ[][][][] ᴀɴᴅ ɪɴᴛʀᴏᴅᴜᴄᴇᴅ ʙʏ ɢᴇʀᴍᴀɴ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄɪᴀɴ ɢᴇᴏʀɢ ᴄᴀɴᴛᴏʀ ɪɴ .[][]

ᴛʜʀᴏᴜɢʜ ᴄᴏɴsɪᴅᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜɪs sᴇᴛ, ᴄᴀɴᴛᴏʀ ᴀɴᴅ ᴏᴛʜᴇʀs ʜᴇʟᴘᴇᴅ ʟᴀʏ ᴛʜᴇ ғᴏᴜɴᴅᴀᴛɪᴏɴs ᴏғ ᴍᴏᴅᴇʀɴ ᴘᴏɪɴᴛ-sᴇᴛ ᴛᴏᴘᴏʟᴏɢʏ. ᴀʟᴛʜᴏᴜɢʜ ᴄᴀɴᴛᴏʀ ʜɪᴍsᴇʟғ ᴅᴇғɪɴᴇᴅ ᴛʜᴇ sᴇᴛ ɪɴ ᴀ ɢᴇɴᴇʀᴀʟ, ᴀʙsᴛʀᴀᴄᴛ ᴡᴀʏ, ᴛʜᴇ ᴍᴏsᴛ ᴄᴏᴍᴍᴏɴ ᴍᴏᴅᴇʀɴ ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ ɪs ᴛʜᴇ ᴄᴀɴᴛᴏʀ ᴛᴇʀɴᴀʀʏ sᴇᴛ, ʙᴜɪʟᴛ ʙʏ ʀᴇᴍᴏᴠɪɴɢ ᴛʜᴇ ᴍɪᴅᴅʟᴇ ᴛʜɪʀᴅ ᴏғ ᴀ ʟɪɴᴇ sᴇɢᴍᴇɴᴛ ᴀɴᴅ ᴛʜᴇɴ ʀᴇᴘᴇᴀᴛɪɴɢ ᴛʜᴇ ᴘʀᴏᴄᴇss ᴡɪᴛʜ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ sʜᴏʀᴛᴇʀ sᴇɢᴍᴇɴᴛs. ᴄᴀɴᴛᴏʀ ʜɪᴍsᴇʟғ ᴍᴇɴᴛɪᴏɴᴇᴅ ᴛʜᴇ ᴛᴇʀɴᴀʀʏ ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ ᴏɴʟʏ ɪɴ ᴘᴀssɪɴɢ, ᴀs ᴀɴ ᴇxᴀᴍᴘʟᴇ ᴏғ ᴀ ᴍᴏʀᴇ ɢᴇɴᴇʀᴀʟ ɪᴅᴇᴀ, ᴛʜᴀᴛ ᴏғ ᴀ ᴘᴇʀғᴇᴄᴛ sᴇᴛ ᴛʜᴀᴛ ɪs ɴᴏᴡʜᴇʀᴇ ᴅᴇɴsᴇ.

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ᴜʜ✌

Answer 2

Step-by-step explanation:

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