Further improve and add in a GUI with other enhancements:

```
--[[
    Transfinite Numerical Computation Framework
    Advanced Roblox Metamathematical Exploration Module
    Developed with Cantorian Set Theoretical Principles
]]

local TransfiniteNumberEngine = {}
TransfiniteNumberEngine.__index = TransfiniteNumberEngine

-- Sophisticated Cardinal Enumeration Mechanism
function TransfiniteNumberEngine.new(initialOrdinal)
    local self = setmetatable({
        _baseCardinal = initialOrdinal or 0,
        _ordinalHierarchy = {},
        _complexityVector = {},
        _metricTensors = {}
    }, TransfiniteNumberEngine)
    
    self:_initializeTransfiniteStructures()
    return self
end

-- Recursive Ordinal Decomposition Algorithm
function TransfiniteNumberEngine:_initializeTransfiniteStructures()
    local function generateRecursiveCardinalMapping(depth)
        if depth > 10 then return nil end
        
        local cardinalMap = {
            base = math.huge,
            successor = math.huge * 2,
            limit = function() 
                return math.huge ^ depth 
            end
        }
        
        return cardinalMap, generateRecursiveCardinalMapping(depth + 1)
    end
    
    self._ordinalHierarchy = generateRecursiveCardinalMapping(1)
end

-- Hyper-Complex Transfinite Transformation
function TransfiniteNumberEngine:computeTransfiniteOperation(operationType, parameters)
    local operationMatrix = {
        ["OMEGA_EXPANSION"] = function(p)
            return math.huge ^ (math.huge ^ p)
        end,
        
        ["EPSILON_PROJECTION"] = function(p)
            return math.huge * math.log(p + 1)
        end,
        
        ["ALEPH_TRANSFORMATION"] = function(p)
            return 2 ^ math.huge * p
        end
    }
    
    local selectedOperation = operationMatrix[operationType] or 
        function() error("Undefined Transfinite Operation") end
    
    local result, status, errorMessage = pcall(function()
        return selectedOperation(parameters)
    end)
    
    if not status then
        warn("Transfinite Computation Error: " .. tostring(errorMessage))
        return nil
    end
    
    return result
end

-- Quantum Probabilistic Error Handling Wrapper
function TransfiniteNumberEngine:safeTransfiniteComputation(computationFunction)
    local function quantumErrorHandler(...)
        local args = {...}
        local success, result = pcall(computationFunction, unpack(args))
        
        if not success then
            warn("Quantum Computation Disruption Detected")
            return nil
        end
        
        return result
    end
    
    return quantumErrorHandler
end

-- Roblox Service Integration
local ReplicatedStorage = game:GetService("ReplicatedStorage")
local TransfiniteRemoteEvent = Instance.new("RemoteEvent")
TransfiniteRemoteEvent.Name = "TransfiniteNumberEvent"
TransfiniteRemoteEvent.Parent = ReplicatedStorage

-- Event Handling Mechanism
TransfiniteRemoteEvent.OnServerEvent:Connect(function(player, computationType, parameters)
    local transfiniteEngine = TransfiniteNumberEngine.new()
    local result = transfiniteEngine:computeTransfiniteOperation(computationType, parameters)
    
    TransfiniteRemoteEvent:FireClient(player, result)
end)

return TransfiniteNumberEngine